1
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Banerjee A, Lesser O, Rahman MA, Thomas C, Wang T, Manfra MJ, Berg E, Oreg Y, Stern A, Marcus CM. Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions. Phys Rev Lett 2023; 130:096202. [PMID: 36930915 DOI: 10.1103/physrevlett.130.096202] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs-Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2×2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the junction, and carrier density. A closing and reopening of a gap was observed in both the local and nonlocal tunneling spectra as a function of magnetic field. For particular tunings of junction density, gap reopenings were accompanied by zero-bias conductance peaks (ZBCPs) in local conductances. End-to-end correlation of gap reopening was strong, while correlation of local ZBCPs was weak. A model of the device, with disorder treated phenomenologically, shows comparable conductance matrix behavior associated with a topological phase transition. Phase dependence helps distinguish possible origins of the ZBCPs.
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Affiliation(s)
- A Banerjee
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - O Lesser
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - M A Rahman
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C Thomas
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
| | - T Wang
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
| | - M J Manfra
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
- School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 USA
| | - E Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - Y Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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2
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Kringhøj A, Winkler GW, Larsen TW, Sabonis D, Erlandsson O, Krogstrup P, van Heck B, Petersson KD, Marcus CM. Andreev Modes from Phase Winding in a Full-Shell Nanowire-Based Transmon. Phys Rev Lett 2021; 126:047701. [PMID: 33576664 DOI: 10.1103/physrevlett.126.047701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2020] [Accepted: 01/07/2021] [Indexed: 06/12/2023]
Abstract
We investigate transmon qubits made from semiconductor nanowires with a fully surrounding superconducting shell. In the regime of reentrant superconductivity associated with the destructive Little-Parks effect, numerous coherent transitions are observed in the first reentrant lobe, where the shell carries 2π winding of superconducting phase, and are absent in the zeroth lobe. As junction density was increased by gate voltage, qubit coherence was suppressed then lost in the first lobe. These observations and numerical simulations highlight the role of winding-induced Andreev states in the junction.
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Affiliation(s)
- A Kringhøj
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - G W Winkler
- Microsoft Quantum, Station Q, University of California, Santa Barbara, California 93106-6105, USA
| | - T W Larsen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - D Sabonis
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - O Erlandsson
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - P Krogstrup
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Materials Lab-Copenhagen, 2800 Lyngby, Denmark
| | - B van Heck
- Microsoft Quantum Lab Delft, Delft University of Technology, 2600 GA Delft, Netherlands
| | - K D Petersson
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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3
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Razmadze D, O'Farrell ECT, Krogstrup P, Marcus CM. Quantum Dot Parity Effects in Trivial and Topological Josephson Junctions. Phys Rev Lett 2020; 125:116803. [PMID: 32975997 DOI: 10.1103/physrevlett.125.116803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2020] [Accepted: 08/10/2020] [Indexed: 06/11/2023]
Abstract
An odd-occupied quantum dot in a Josephson junction can flip transmission phase, creating a π junction. When the junction couples topological superconductors, no phase flip is expected. We investigate this and related effects in a full-shell hybrid interferometer, using gate voltage to control dot-junction parity and axial magnetic flux to control the transition from trivial to topological superconductivity. Enhanced zero-bias conductance and critical current for odd parity in the topological phase reflects hybridization of the confined spin with zero-energy modes in the leads.
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Affiliation(s)
- D Razmadze
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, 2100 Copenhagen, Denmark
| | - E C T O'Farrell
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, 2100 Copenhagen, Denmark
| | - P Krogstrup
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Materials Lab-Copenhagen, 2800 Kongens Lyngby, Denmark
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Lab-Copenhagen, 2100 Copenhagen, Denmark
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4
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Larsen TW, Gershenson ME, Casparis L, Kringhøj A, Pearson NJ, McNeil RPG, Kuemmeth F, Krogstrup P, Petersson KD, Marcus CM. Parity-Protected Superconductor-Semiconductor Qubit. Phys Rev Lett 2020; 125:056801. [PMID: 32794832 DOI: 10.1103/physrevlett.125.056801] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 07/09/2020] [Indexed: 06/11/2023]
Abstract
Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2φ) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.
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Affiliation(s)
- T W Larsen
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - M E Gershenson
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - L Casparis
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - A Kringhøj
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - N J Pearson
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
| | - R P G McNeil
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - F Kuemmeth
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - P Krogstrup
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Microsoft Quantum Materials Lab-Copenhagen, 2800 Kongens Lyngby, Denmark
| | - K D Petersson
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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5
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Whiticar AM, Fornieri A, O'Farrell ECT, Drachmann ACC, Wang T, Thomas C, Gronin S, Kallaher R, Gardner GC, Manfra MJ, Marcus CM, Nichele F. Coherent transport through a Majorana island in an Aharonov-Bohm interferometer. Nat Commun 2020; 11:3212. [PMID: 32587242 PMCID: PMC7316771 DOI: 10.1038/s41467-020-16988-x] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2020] [Accepted: 05/17/2020] [Indexed: 11/29/2022] Open
Abstract
Majorana zero modes are leading candidates for topological quantum computation due to non-local qubit encoding and non-abelian exchange statistics. Spatially separated Majorana modes are expected to allow phase-coherent single-electron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally investigate such a system by patterning an elongated epitaxial InAs-Al island embedded in an Aharonov-Bohm interferometer. With increasing parallel magnetic field, a discrete sub-gap state in the island is lowered to zero energy yielding persistent 1e-periodic Coulomb blockade conductance peaks (e is the elementary charge). In this condition, conductance through the interferometer is observed to oscillate in a perpendicular magnetic field with a flux period of h/e (h is Planck’s constant), indicating coherent transport of single electrons through the islands, a signature of electron teleportation via Majorana modes. Theories predict teleportation of phase-coherent single electrons through a topological superconducting island. Here, the authors report persistent Coulomb blockade conductance peaks due to coherent transport of single electrons through patterned InAs-Al islands embedded in an Aharonov-Bohm interferometer.
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Affiliation(s)
- A M Whiticar
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen and Microsoft Quantum Lab Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark
| | - A Fornieri
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen and Microsoft Quantum Lab Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark
| | - E C T O'Farrell
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen and Microsoft Quantum Lab Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark
| | - A C C Drachmann
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen and Microsoft Quantum Lab Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark
| | - T Wang
- Department of Physics and Astronomy and Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN, 47907, USA.,Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - C Thomas
- Department of Physics and Astronomy and Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN, 47907, USA.,Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - S Gronin
- Department of Physics and Astronomy and Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN, 47907, USA.,Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - R Kallaher
- Department of Physics and Astronomy and Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN, 47907, USA.,Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - G C Gardner
- Department of Physics and Astronomy and Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN, 47907, USA.,Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - M J Manfra
- Department of Physics and Astronomy and Microsoft Quantum Lab Purdue, Purdue University, West Lafayette, IN, 47907, USA.,Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA.,School of Materials Engineering, Purdue University, West Lafayette, IN, 47907, USA.,School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907, USA
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen and Microsoft Quantum Lab Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark.
| | - F Nichele
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen and Microsoft Quantum Lab Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark. .,IBM Research - Zurich, Sumerstrasse 4, 8803, Rschlikon, Switzerland.
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6
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Kringhøj A, van Heck B, Larsen TW, Erlandsson O, Sabonis D, Krogstrup P, Casparis L, Petersson KD, Marcus CM. Suppressed Charge Dispersion via Resonant Tunneling in a Single-Channel Transmon. Phys Rev Lett 2020; 124:246803. [PMID: 32639819 DOI: 10.1103/physrevlett.124.246803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2019] [Accepted: 05/15/2020] [Indexed: 06/11/2023]
Abstract
We demonstrate strong suppression of charge dispersion in a semiconductor-based transmon qubit across Josephson resonances associated with a quantum dot in the junction. On resonance, dispersion is drastically reduced compared to conventional transmons with corresponding Josephson and charging energies. We develop a model of qubit dispersion for a single-channel resonance, which is in quantitative agreement with experimental data.
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Affiliation(s)
- A Kringhøj
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - B van Heck
- Microsoft Quantum, Station Q, University of California, Santa Barbara, California 93106-6105, USA
- Microsoft Quantum Lab Delft, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - T W Larsen
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - O Erlandsson
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - D Sabonis
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - P Krogstrup
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum Materials Lab Copenhagen, Kanalvej 7, 2800 Lyngby, Denmark
| | - L Casparis
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - K D Petersson
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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7
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Nichele F, Portolés E, Fornieri A, Whiticar AM, Drachmann ACC, Gronin S, Wang T, Gardner GC, Thomas C, Hatke AT, Manfra MJ, Marcus CM. Relating Andreev Bound States and Supercurrents in Hybrid Josephson Junctions. Phys Rev Lett 2020; 124:226801. [PMID: 32567899 DOI: 10.1103/physrevlett.124.226801] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Revised: 03/03/2020] [Accepted: 04/27/2020] [Indexed: 06/11/2023]
Abstract
We demonstrate concomitant measurement of phase-dependent critical current and Andreev bound state spectrum in a highly transmissive InAs Josephson junction embedded in a dc superconducting quantum interference device (SQUID). Tunneling spectroscopy reveals Andreev bound states with near unity transmission probability. A nonsinusoidal current-phase relation is derived from the Andreev spectrum, showing excellent agreement with the one extracted from the SQUID critical current. Both measurements are reconciled within a short junction model where multiple Andreev bound states, with various transmission probabilities, contribute to the entire supercurrent flowing in the junction.
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Affiliation(s)
- F Nichele
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- IBM Research-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - E Portolés
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A Fornieri
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A M Whiticar
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A C C Drachmann
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - S Gronin
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - T Wang
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - C Thomas
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - A T Hatke
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - M J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - C M Marcus
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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8
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Vaitiekėnas S, Winkler GW, van Heck B, Karzig T, Deng MT, Flensberg K, Glazman LI, Nayak C, Krogstrup P, Lutchyn RM, Marcus CM. Flux-induced topological superconductivity in full-shell nanowires. Science 2020; 367:367/6485/eaav3392. [DOI: 10.1126/science.aav3392] [Citation(s) in RCA: 90] [Impact Index Per Article: 22.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2018] [Revised: 08/04/2019] [Accepted: 02/27/2020] [Indexed: 11/02/2022]
Abstract
Hybrid semiconductor-superconductor nanowires have emerged as a promising platform for realizing topological superconductivity (TSC). Here, we present a route to TSC using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zero-energy state around one applied flux quantum, corresponding to 2π phase winding. Theoretical analysis indicates that the winding of the superconducting phase can induce a transition to a topological phase supporting Majorana zero modes. Measured Coulomb blockade peak spacing around one flux quantum shows a length dependence that is consistent with the existence of Majorana modes at the ends of the nanowire.
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Affiliation(s)
- S. Vaitiekėnas
- Center for Quantum Devices and Microsoft Quantum Lab–Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - G. W. Winkler
- Microsoft Quantum, Microsoft Station Q, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - B. van Heck
- Microsoft Quantum, Microsoft Station Q, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - T. Karzig
- Microsoft Quantum, Microsoft Station Q, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - M.-T. Deng
- Center for Quantum Devices and Microsoft Quantum Lab–Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - K. Flensberg
- Center for Quantum Devices and Microsoft Quantum Lab–Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - L. I. Glazman
- Departments of Physics and Applied Physics, Yale University, New Haven, CT 06520, USA
| | - C. Nayak
- Microsoft Quantum, Microsoft Station Q, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - P. Krogstrup
- Center for Quantum Devices and Microsoft Quantum Lab–Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - R. M. Lutchyn
- Microsoft Quantum, Microsoft Station Q, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - C. M. Marcus
- Center for Quantum Devices and Microsoft Quantum Lab–Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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9
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Kringhøj A, Larsen TW, van Heck B, Sabonis D, Erlandsson O, Petkovic I, Pikulin DI, Krogstrup P, Petersson KD, Marcus CM. Controlled dc Monitoring of a Superconducting Qubit. Phys Rev Lett 2020; 124:056801. [PMID: 32083909 DOI: 10.1103/physrevlett.124.056801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Accepted: 12/23/2019] [Indexed: 06/10/2023]
Abstract
Creating a transmon qubit using semiconductor-superconductor hybrid materials not only provides electrostatic control of the qubit frequency, it also allows parts of the circuit to be electrically connected and disconnected in situ by operating a semiconductor region of the device as a field-effect transistor. Here, we exploit this feature to compare in the same device characteristics of the qubit, such as frequency and relaxation time, with related transport properties such as critical supercurrent and normal-state resistance. Gradually opening the field-effect transistor to the monitoring circuit allows the influence of weak-to-strong dc monitoring of a "live" qubit to be measured. A model of this influence yields excellent agreement with experiment, demonstrating a relaxation rate mediated by a gate-controlled environmental coupling.
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Affiliation(s)
- A Kringhøj
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - T W Larsen
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - B van Heck
- Microsoft Quantum, Station Q, University of California, Santa Barbara, California 93106-6105, USA
- Microsoft Quantum Lab Delft, Delft University of Technology, 2600 GA Delft, Netherlands
| | - D Sabonis
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - O Erlandsson
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - I Petkovic
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - D I Pikulin
- Microsoft Quantum, Station Q, University of California, Santa Barbara, California 93106-6105, USA
| | - P Krogstrup
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum Materials Lab Copenhagen, Kanalvej 7, 2800 Lyngby, Denmark
| | - K D Petersson
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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10
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Ménard GC, Anselmetti GLR, Martinez EA, Puglia D, Malinowski FK, Lee JS, Choi S, Pendharkar M, Palmstrøm CJ, Flensberg K, Marcus CM, Casparis L, Higginbotham AP. Conductance-Matrix Symmetries of a Three-Terminal Hybrid Device. Phys Rev Lett 2020; 124:036802. [PMID: 32031865 DOI: 10.1103/physrevlett.124.036802] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Indexed: 06/10/2023]
Abstract
We present conductance-matrix measurements of a three-terminal superconductor-semiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that antisymmetric components of pairs of local and nonlocal conductances qualitatively match at energies below the superconducting gap, and we compare this finding with symmetry relations based on a noninteracting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetry-decomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in low-energy features, demonstrating how conductance-matrix measurements can complement traditional single-probe measurements in the search for Majorana zero modes.
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Affiliation(s)
- G C Ménard
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - G L R Anselmetti
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - E A Martinez
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - D Puglia
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F K Malinowski
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J S Lee
- California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA
| | - S Choi
- Department of Electrical Engineering, University of California, Santa Barbara, California 93106, USA
| | - M Pendharkar
- Department of Electrical Engineering, University of California, Santa Barbara, California 93106, USA
| | - C J Palmstrøm
- California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA
- Department of Electrical Engineering, University of California, Santa Barbara, California 93106, USA
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - K Flensberg
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - L Casparis
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A P Higginbotham
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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11
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O'Farrell ECT, Drachmann ACC, Hell M, Fornieri A, Whiticar AM, Hansen EB, Gronin S, Gardner GC, Thomas C, Manfra MJ, Flensberg K, Marcus CM, Nichele F. Hybridization of Subgap States in One-Dimensional Superconductor-Semiconductor Coulomb Islands. Phys Rev Lett 2018; 121:256803. [PMID: 30608825 DOI: 10.1103/physrevlett.121.256803] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2018] [Indexed: 06/09/2023]
Abstract
We present measurements of one-dimensional superconductor-semiconductor Coulomb islands, fabricated by gate confinement of a two-dimensional InAs heterostructure with an epitaxial Al layer. When tuned via electrostatic side gates to regimes without subgap states, Coulomb blockade reveals Cooper-pair mediated transport. When subgap states are present, Coulomb peak positions and heights oscillate in a correlated way with magnetic field and gate voltage, as predicted theoretically, with (anti)crossings in (parallel) transverse magnetic field indicating Rashba-type spin-orbit coupling. Overall results are consistent with a picture of overlapping Majorana zero modes in finite wires.
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Affiliation(s)
- E C T O'Farrell
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A C C Drachmann
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M Hell
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Division of Solid State Physics and NanoLund, Lund University, Box 118, S-22100 Lund, Sweden
| | - A Fornieri
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A M Whiticar
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - E B Hansen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - S Gronin
- Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - C Thomas
- Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - M J Manfra
- Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - K Flensberg
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F Nichele
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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12
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Vaitiekėnas S, Whiticar AM, Deng MT, Krizek F, Sestoft JE, Palmstrøm CJ, Marti-Sanchez S, Arbiol J, Krogstrup P, Casparis L, Marcus CM. Selective-Area-Grown Semiconductor-Superconductor Hybrids: A Basis for Topological Networks. Phys Rev Lett 2018; 121:147701. [PMID: 30339420 DOI: 10.1103/physrevlett.121.147701] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2018] [Revised: 06/20/2018] [Indexed: 06/08/2023]
Abstract
We introduce selective area grown hybrid InAs/Al nanowires based on molecular beam epitaxy, allowing arbitrary semiconductor-superconductor networks containing loops and branches. Transport reveals a hard induced gap and unpoisoned 2e-periodic Coulomb blockade, with temperature dependent 1e features in agreement with theory. Coulomb peak spacing in parallel magnetic field displays overshoot, indicating an oscillating discrete near-zero subgap state consistent with device length. Finally, we investigate a loop network, finding strong spin-orbit coupling and a coherence length of several microns. These results demonstrate the potential of this platform for scalable topological networks among other applications.
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Affiliation(s)
- S Vaitiekėnas
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A M Whiticar
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M-T Deng
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F Krizek
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J E Sestoft
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C J Palmstrøm
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - S Marti-Sanchez
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, 08193 Bellaterra, Barcelona, Spain
| | - J Arbiol
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, 08193 Bellaterra, Barcelona, Spain
- ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Catalonia, Spain
| | - P Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - L Casparis
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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13
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Vaitiekėnas S, Deng MT, Nygård J, Krogstrup P, Marcus CM. Effective g Factor of Subgap States in Hybrid Nanowires. Phys Rev Lett 2018; 121:037703. [PMID: 30085813 DOI: 10.1103/physrevlett.121.037703] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Revised: 12/16/2017] [Indexed: 06/08/2023]
Abstract
We use the effective g factor of Andreev subgap states in an axial magnetic field to investigate how the superconducting density of states is distributed between the semiconductor core and the superconducting shell in hybrid nanowires. We find a steplike reduction of the Andreev g factor and an improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and a g factor exceeding that of the parent superconductor.
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Affiliation(s)
- S Vaitiekėnas
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M-T Deng
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J Nygård
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - P Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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14
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Suominen HJ, Kjaergaard M, Hamilton AR, Shabani J, Palmstrøm CJ, Marcus CM, Nichele F. Zero-Energy Modes from Coalescing Andreev States in a Two-Dimensional Semiconductor-Superconductor Hybrid Platform. Phys Rev Lett 2017; 119:176805. [PMID: 29219474 DOI: 10.1103/physrevlett.119.176805] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2017] [Indexed: 06/07/2023]
Abstract
We investigate zero-bias conductance peaks that arise from coalescing subgap Andreev states, consistent with emerging Majorana zero modes, in hybrid semiconductor-superconductor wires defined in a two-dimensional InAs/Al heterostructure using top-down lithography and gating. The measurements indicate a hard superconducting gap, ballistic tunneling contact, and in-plane critical fields up to 3 T. Top-down lithography allows complex geometries, branched structures, and straightforward scaling to multicomponent devices compared to structures made from assembled nanowires.
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Affiliation(s)
- H J Suominen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M Kjaergaard
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A R Hamilton
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - J Shabani
- California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA
- Center for Quantum Phenomena, Physics Department, New York University, New York 10031, USA
| | - C J Palmstrøm
- California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA
- Department of Electrical Engineering, University of California, Santa Barbara, California 93106, USA
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F Nichele
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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15
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Albrecht SM, Hansen EB, Higginbotham AP, Kuemmeth F, Jespersen TS, Nygård J, Krogstrup P, Danon J, Flensberg K, Marcus CM. Transport Signatures of Quasiparticle Poisoning in a Majorana Island. Phys Rev Lett 2017; 118:137701. [PMID: 28409973 DOI: 10.1103/physrevlett.118.137701] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2016] [Indexed: 06/07/2023]
Abstract
We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (∼1 μs) and sets a bound for a weakly coupled island (>10 μs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. When converted from gate voltage to energy units, fluctuations are consistent with previous measurements.
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Affiliation(s)
- S M Albrecht
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - E B Hansen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - A P Higginbotham
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
- JILA, University of Colorado and NIST, Boulder, Colorado 80309, USA
| | - F Kuemmeth
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - T S Jespersen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - J Nygård
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - P Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - J Danon
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
- Department of Physics, NTNU, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - K Flensberg
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
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16
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Sherman D, Yodh JS, Albrecht SM, Nygård J, Krogstrup P, Marcus CM. Normal, superconducting and topological regimes of hybrid double quantum dots. Nat Nanotechnol 2017; 12:212-217. [PMID: 27842064 DOI: 10.1038/nnano.2016.227] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Accepted: 09/19/2016] [Indexed: 06/06/2023]
Abstract
Epitaxial semiconductor-superconductor hybrid materials are an excellent basis for studying mesoscopic and topological superconductivity, as the semiconductor inherits a hard superconducting gap while retaining tunable carrier density. Here, we investigate double-quantum-dot structures made from InAs nanowires with a patterned epitaxial Al two-facet shell that proximitizes two gate-defined segments along the nanowire. We follow the evolution of mesoscopic superconductivity and charging energy in this system as a function of magnetic field and voltage-tuned barriers. Interdot coupling is varied from strong to weak using side gates, and the ground state is varied between normal, superconducting and topological regimes by applying a magnetic field. We identify the topological transition by tracking the spacing between successive co-tunnelling peaks as a function of axial magnetic field and show that the individual dots host weakly hybridized Majorana modes.
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Affiliation(s)
- D Sherman
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - J S Yodh
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - S M Albrecht
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - J Nygård
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - P Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
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17
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Drachmann ACC, Suominen HJ, Kjaergaard M, Shojaei B, Palmstrøm CJ, Marcus CM, Nichele F. Proximity Effect Transfer from NbTi into a Semiconductor Heterostructure via Epitaxial Aluminum. Nano Lett 2017; 17:1200-1203. [PMID: 28072541 DOI: 10.1021/acs.nanolett.6b04964] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We demonstrate the transfer of the superconducting properties of NbTi, a large-gap high-critical-field superconductor, into an InAs heterostructure via a thin intermediate layer of epitaxial Al. Two device geometries, a Josephson junction and a gate-defined quantum point contact, are used to characterize interface transparency and the two-step proximity effect. In the Josephson junction, multiple Andreev reflections reveal near-unity transparency with an induced gap Δ* = 0.50 meV and a critical temperature of 7.8 K. Tunneling spectroscopy yields a hard induced gap in the InAs adjacent to the superconductor of Δ* = 0.43 meV with substructure characteristic of both Al and NbTi.
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Affiliation(s)
- A C C Drachmann
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute University of Copenhagen , Universitetsparken 5, 2100 Copenhagen, Denmark
| | - H J Suominen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute University of Copenhagen , Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M Kjaergaard
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute University of Copenhagen , Universitetsparken 5, 2100 Copenhagen, Denmark
| | | | | | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute University of Copenhagen , Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F Nichele
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute University of Copenhagen , Universitetsparken 5, 2100 Copenhagen, Denmark
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18
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Deng MT, Vaitiekėnas S, Hansen EB, Danon J, Leijnse M, Flensberg K, Nygård J, Krogstrup P, Marcus CM. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 2016; 354:1557-1562. [DOI: 10.1126/science.aaf3961] [Citation(s) in RCA: 687] [Impact Index Per Article: 85.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2016] [Accepted: 11/16/2016] [Indexed: 11/02/2022]
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19
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Kjaergaard M, Nichele F, Suominen HJ, Nowak MP, Wimmer M, Akhmerov AR, Folk JA, Flensberg K, Shabani J, Palmstrøm CJ, Marcus CM. Quantized conductance doubling and hard gap in a two-dimensional semiconductor-superconductor heterostructure. Nat Commun 2016; 7:12841. [PMID: 27682268 PMCID: PMC5056412 DOI: 10.1038/ncomms12841] [Citation(s) in RCA: 121] [Impact Index Per Article: 15.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2016] [Accepted: 08/08/2016] [Indexed: 12/11/2022] Open
Abstract
Coupling a two-dimensional (2D) semiconductor heterostructure to a superconductor opens new research and technology opportunities, including fundamental problems in mesoscopic superconductivity, scalable superconducting electronics, and new topological states of matter. One route towards topological matter is by coupling a 2D electron gas with strong spin–orbit interaction to an s-wave superconductor. Previous efforts along these lines have been adversely affected by interface disorder and unstable gating. Here we show measurements on a gateable InGaAs/InAs 2DEG with patterned epitaxial Al, yielding devices with atomically pristine interfaces between semiconductor and superconductor. Using surface gates to form a quantum point contact (QPC), we find a hard superconducting gap in the tunnelling regime. When the QPC is in the open regime, we observe a first conductance plateau at 4e2/h, consistent with theory. The hard-gap semiconductor–superconductor system demonstrated here is amenable to top-down processing and provides a new avenue towards low-dissipation electronics and topological quantum systems. Interface transparency between 2D semiconductors and superconductors is a longstanding problem, seriously hindering potential applications. Here, using a new hybrid system, Kjaergaard et al. report quantized conductance doubling and a hard superconducting gap measured via a quantum point contact, indicating a near pristine interface.
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Affiliation(s)
- M Kjaergaard
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F Nichele
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - H J Suominen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M P Nowak
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 4056, 2600 GA Delft, The Netherlands.,QuTech, Delft University of Technology, PO Box 4056, 2600 GA Delft, The Netherlands.,AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Mickiewicza 30, 30-059 Kraków, Poland
| | - M Wimmer
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 4056, 2600 GA Delft, The Netherlands.,QuTech, Delft University of Technology, PO Box 4056, 2600 GA Delft, The Netherlands
| | - A R Akhmerov
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 4056, 2600 GA Delft, The Netherlands
| | - J A Folk
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T1Z1.,Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada V6T1Z4
| | - K Flensberg
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J Shabani
- California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA
| | - C J Palmstrøm
- California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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20
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Casparis L, Larsen TW, Olsen MS, Kuemmeth F, Krogstrup P, Nygård J, Petersson KD, Marcus CM. Gatemon Benchmarking and Two-Qubit Operations. Phys Rev Lett 2016; 116:150505. [PMID: 27127949 DOI: 10.1103/physrevlett.116.150505] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2015] [Indexed: 06/05/2023]
Abstract
Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic of semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors below 0.7% for all gates, including voltage-controlled Z rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a two-qubit controlled-phase gate with an estimated fidelity of 91%, demonstrating the potential of gatemon qubits for building scalable quantum processors.
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Affiliation(s)
- L Casparis
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - T W Larsen
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - M S Olsen
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - F Kuemmeth
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - P Krogstrup
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - J Nygård
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
- Nano-Science Center, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - K D Petersson
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
| | - C M Marcus
- Center for Quantum Devices, Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
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21
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Albrecht SM, Higginbotham AP, Madsen M, Kuemmeth F, Jespersen TS, Nygård J, Krogstrup P, Marcus CM. Exponential protection of zero modes in Majorana islands. Nature 2016; 531:206-9. [DOI: 10.1038/nature17162] [Citation(s) in RCA: 770] [Impact Index Per Article: 96.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2015] [Accepted: 01/18/2016] [Indexed: 11/09/2022]
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22
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Larsen TW, Petersson KD, Kuemmeth F, Jespersen TS, Krogstrup P, Nygård J, Marcus CM. Semiconductor-Nanowire-Based Superconducting Qubit. Phys Rev Lett 2015; 115:127001. [PMID: 26431009 DOI: 10.1103/physrevlett.115.127001] [Citation(s) in RCA: 99] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2015] [Indexed: 06/05/2023]
Abstract
We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmonlike device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an on-chip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (~0.8 μs) and dephasing times (~1 μs), exceeding gate operation times by 2 orders of magnitude, in these first-generation devices. Because qubit control relies on voltages rather than fluxes, dissipation in resistive control lines is reduced, screening reduces cross talk, and the absence of flux control allows operation in a magnetic field, relevant for topological quantum information.
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Affiliation(s)
- T W Larsen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - K D Petersson
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - F Kuemmeth
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - T S Jespersen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - P Krogstrup
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - J Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
- Nano-Science Center, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
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23
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Krogstrup P, Ziino NLB, Chang W, Albrecht SM, Madsen MH, Johnson E, Nygård J, Marcus CM, Jespersen TS. Epitaxy of semiconductor-superconductor nanowires. Nat Mater 2015; 14:400-6. [PMID: 25581626 DOI: 10.1038/nmat4176] [Citation(s) in RCA: 147] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2014] [Accepted: 11/18/2014] [Indexed: 05/05/2023]
Abstract
Controlling the properties of semiconductor/metal interfaces is a powerful method for designing functionality and improving the performance of electrical devices. Recently semiconductor/superconductor hybrids have appeared as an important example where the atomic scale uniformity of the interface plays a key role in determining the quality of the induced superconducting gap. Here we present epitaxial growth of semiconductor-metal core-shell nanowires by molecular beam epitaxy, a method that provides a conceptually new route to controlled electrical contacting of nanostructures and the design of devices for specialized applications such as topological and gate-controlled superconducting electronics. Our materials of choice, InAs/Al grown with epitaxially matched single-plane interfaces, and alternative semiconductor/metal combinations allowing epitaxial interface matching in nanowires are discussed. We formulate the grain growth kinetics of the metal phase in general terms of continuum parameters and bicrystal symmetries. The method realizes the ultimate limit of uniform interfaces and seems to solve the soft-gap problem in superconducting hybrid structures.
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Affiliation(s)
- P Krogstrup
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - N L B Ziino
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - W Chang
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - S M Albrecht
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - M H Madsen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - E Johnson
- 1] Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark [2] Department of Wind Energy, Technical University of Denmark, Risø Campus, 4000 Roskilde, Denmark
| | - J Nygård
- 1] Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark [2] Nano-Science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - T S Jespersen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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24
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Chang W, Albrecht SM, Jespersen TS, Kuemmeth F, Krogstrup P, Nygård J, Marcus CM. Hard gap in epitaxial semiconductor-superconductor nanowires. Nat Nanotechnol 2015; 10:232-236. [PMID: 25581886 DOI: 10.1038/nnano.2014.306] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2014] [Accepted: 11/18/2014] [Indexed: 06/04/2023]
Abstract
Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunnelling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on the proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunnelling conductance below the superconducting gap, suggesting a continuum of subgap states--a situation that nullifies topological protection. Here, we report a hard superconducting gap induced by the proximity effect in a semiconductor, using epitaxial InAs-Al semiconductor-superconductor nanowires. The hard gap, together with favourable material properties and gate-tunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.
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Affiliation(s)
- W Chang
- 1] Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark [2] Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - S M Albrecht
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - T S Jespersen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F Kuemmeth
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - P Krogstrup
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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25
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Higginbotham AP, Larsen TW, Yao J, Yan H, Lieber CM, Marcus CM, Kuemmeth F. Hole spin coherence in a Ge/Si heterostructure nanowire. Nano Lett 2014; 14:3582-6. [PMID: 24797219 DOI: 10.1021/nl501242b] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Relaxation and dephasing of hole spins are measured in a gate-defined Ge/Si nanowire double quantum dot using a fast pulsed-gate method and dispersive readout. An inhomogeneous dephasing time T2* 0.18 μs exceeds corresponding measurements in III–V semiconductors by more than an order of magnitude, as expected for predominately nuclear-spin-free materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclear-spin-dominated dephasing.
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Affiliation(s)
- A P Higginbotham
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen , 2100 Copenhagen, Denmark
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26
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Higginbotham AP, Kuemmeth F, Hanson MP, Gossard AC, Marcus CM. Coherent operations and screening in multielectron spin qubits. Phys Rev Lett 2014; 112:026801. [PMID: 24484035 DOI: 10.1103/physrevlett.112.026801] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2013] [Indexed: 06/03/2023]
Abstract
Multielectron spin qubits are demonstrated, and performance examined by comparing coherent exchange oscillations in coupled single-electron and multielectron quantum dots, measured in the same device. Fast (>1 GHz) exchange oscillations with a quality factor Q∼15 are found for the multielectron case, compared to Q∼2 for the single-electron case, the latter consistent with experiments in the literature. A model of dephasing that includes voltage and hyperfine noise is developed that is in good agreement with both single- and multielectron data, though in both cases additional exchange-independent dephasing is needed to obtain quantitative agreement across a broad parameter range.
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Affiliation(s)
- A P Higginbotham
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA and Center for Quantum Devices, Niels Bohr Institute, 2100 Copenhagen, Denmark
| | - F Kuemmeth
- Center for Quantum Devices, Niels Bohr Institute, 2100 Copenhagen, Denmark
| | - M P Hanson
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - A C Gossard
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, 2100 Copenhagen, Denmark
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27
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Medford J, Beil J, Taylor JM, Bartlett SD, Doherty AC, Rashba EI, DiVincenzo DP, Lu H, Gossard AC, Marcus CM. Self-consistent measurement and state tomography of an exchange-only spin qubit. Nat Nanotechnol 2013; 8:654-659. [PMID: 23995458 DOI: 10.1038/nnano.2013.168] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2013] [Accepted: 07/20/2013] [Indexed: 06/02/2023]
Abstract
Quantum-dot spin qubits characteristically use oscillating magnetic or electric fields, or quasi-static Zeeman field gradients, to realize full qubit control. For the case of three confined electrons, exchange interaction between two pairs allows qubit rotation around two axes, hence full control, using only electrostatic gates. Here, we report initialization, full control, and single-shot readout of a three-electron exchange-driven spin qubit. Control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in less than 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements and non-orthogonal control axes.
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Affiliation(s)
- J Medford
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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28
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Medford J, Beil J, Taylor JM, Rashba EI, Lu H, Gossard AC, Marcus CM. Quantum-dot-based resonant exchange qubit. Phys Rev Lett 2013; 111:050501. [PMID: 23952375 DOI: 10.1103/physrevlett.111.050501] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2013] [Indexed: 06/02/2023]
Abstract
We introduce a solid-state qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gate-voltage pulses. We demonstrate two-axis control at a detuning sweet spot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A π/2-gate time of 2.5 ns and a coherence time of 19 μs, using multipulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment.
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Affiliation(s)
- J Medford
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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29
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Chang W, Manucharyan VE, Jespersen TS, Nygård J, Marcus CM. Tunneling spectroscopy of quasiparticle bound states in a spinful Josephson junction. Phys Rev Lett 2013; 110:217005. [PMID: 23745916 DOI: 10.1103/physrevlett.110.217005] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2012] [Indexed: 06/02/2023]
Abstract
The spectrum of a segment of InAs nanowire, confined between two superconducting leads, was measured as function of gate voltage and superconducting phase difference using a third normal-metal tunnel probe. Subgap resonances for odd electron occupancy-interpreted as bound states involving a confined electron and a quasiparticle from the superconducting leads, reminiscent of Yu-Shiba-Rusinov states-evolve into Kondo-related resonances at higher magnetic fields. An additional zero-bias peak of unknown origin is observed to coexist with the quasiparticle bound states.
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Affiliation(s)
- W Chang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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30
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Cassidy MC, Chan HR, Ross BD, Bhattacharya PK, Marcus CM. In vivo magnetic resonance imaging of hyperpolarized silicon particles. Nat Nanotechnol 2013; 8:363-368. [PMID: 23644571 DOI: 10.1038/nnano.2013.65] [Citation(s) in RCA: 77] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2012] [Accepted: 03/19/2013] [Indexed: 06/02/2023]
Abstract
Silicon-based micro- and nanoparticles have gained popularity in a wide range of biomedical applications due to their biocompatibility and biodegradability in vivo, as well as their flexible surface chemistry, which allows drug loading, functionalization and targeting. Here, we report direct in vivo imaging of hyperpolarized (29)Si nuclei in silicon particles by magnetic resonance imaging. Natural physical properties of silicon provide surface electronic states for dynamic nuclear polarization, extremely long depolarization times, insensitivity to the in vivo environment or particle tumbling, and surfaces favourable for functionalization. Potential applications to gastrointestinal, intravascular and tumour perfusion imaging at subpicomolar concentrations are presented. These results demonstrate a new background-free imaging modality applicable to a range of inexpensive, readily available and biocompatible silicon particles.
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Affiliation(s)
- M C Cassidy
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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31
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Kou A, Marcus CM, Pfeiffer LN, West KW. Coulomb oscillations in antidots in the integer and fractional quantum Hall regimes. Phys Rev Lett 2012; 108:256803. [PMID: 23004632 DOI: 10.1103/physrevlett.108.256803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2012] [Indexed: 06/01/2023]
Abstract
We report measurements of resistance oscillations in micron-scale antidots in both the integer and fractional quantum Hall regimes. In the integer regime, we conclude that oscillations are of the Coulomb type from the scaling of magnetic field period with the number of edges bound to the antidot. Based on both gate-voltage and field periods, we find at filling factor ν = 2 a tunneling charge of e and two charged edges. Generalizing this picture to the fractional regime, we find (again, based on field and gate-voltage periods) at ν = 2/3 a tunneling charge of (2/3)e and a single charged edge.
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Affiliation(s)
- A Kou
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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32
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McClure DT, Chang W, Marcus CM, Pfeiffer LN, West KW. Fabry-Perot interferometry with fractional charges. Phys Rev Lett 2012; 108:256804. [PMID: 23004633 DOI: 10.1103/physrevlett.108.256804] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2011] [Indexed: 06/01/2023]
Abstract
Resistance oscillations in electronic Fabry-Perot interferometers near fractional quantum Hall (FQH) filling factors 1/3, 2/3, 4/3, and 5/3 in the constrictions are compared to those near integer quantum Hall (IQH) filling factors in the same devices and at the same gate voltages. Two-dimensional plots of resistance versus gate voltage and magnetic field indicate that all oscillations are Coulomb dominated. A charging-model analysis of gate-voltage periods yields an effective tunneling charge e* ≈ e/3 for all FQH states and e* ≈ e for IQH states. Temperature decay of the oscillations appears exponential, qualitatively consistent with a recent prediction, and the surprising filling-factor dependence of the associated energy scale may shed light on edge structure.
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Affiliation(s)
- D T McClure
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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33
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Medford J, Cywiński Ł, Barthel C, Marcus CM, Hanson MP, Gossard AC. Scaling of dynamical decoupling for spin qubits. Phys Rev Lett 2012; 108:086802. [PMID: 22463554 DOI: 10.1103/physrevlett.108.086802] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2011] [Indexed: 05/31/2023]
Abstract
We investigate the scaling of coherence time T(2) with the number of π pulses n(π) in a singlet-triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law T(2) is proportional to (n(π))(γ(e)), with γ(e)=0.72±0.01, essentially independent of the envelope function used to extract T(2). From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S(ω)~ω(-β), yields β=γ(e)/(1-γ(e))=2.6±0.1. Model values for T(2)(n(π)) using β=2.6 for CPMG with both even and odd n(π) up to 32 and CDD orders 3 through 6 compare very well with the experiment.
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Affiliation(s)
- J Medford
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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34
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Taylor JM, Sørensen AS, Marcus CM, Polzik ES. Laser cooling and optical detection of excitations in a LC electrical circuit. Phys Rev Lett 2011; 107:273601. [PMID: 22243310 DOI: 10.1103/physrevlett.107.273601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2011] [Indexed: 05/31/2023]
Abstract
We explore a method for laser cooling and optical detection of excitations in a room temperature LC electrical circuit. Our approach uses a nanomechanical oscillator as a transducer between optical and electronic excitations. An experimentally feasible system with the oscillator capacitively coupled to the LC and at the same time interacting with light via an optomechanical force is shown to provide strong electromechanical coupling. Conditions for improved sensitivity and quantum limited readout of electrical signals with such an "optical loud speaker" are outlined.
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Affiliation(s)
- J M Taylor
- Joint Quantum Institute/NIST, College Park, Maryland, USA
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35
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Abstract
We investigate transport in locally gated graphene devices, where carriers are injected and collected along, rather than across, the gate edge. Tuning densities into the p-n regime significantly reduces resistance along the p-n interface, while resistance across the interface increases. This provides an experimental signature of snake states, which zigzag along the p-n interface and remain stable as applied perpendicular magnetic field approaches zero. Snake states appear as a peak in transverse resistance measured along the p-n interface. The generic role of snake states in disordered graphene is also discussed.
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Affiliation(s)
- J R Williams
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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36
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van Weperen I, Armstrong BD, Laird EA, Medford J, Marcus CM, Hanson MP, Gossard AC. Charge-state conditional operation of a spin qubit. Phys Rev Lett 2011; 107:030506. [PMID: 21838342 DOI: 10.1103/physrevlett.107.030506] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2011] [Indexed: 05/31/2023]
Abstract
We report coherent operation of a singlet-triplet qubit controlled by the spatial arrangement of two confined electrons in an adjacent double quantum dot that is electrostatically coupled to the qubit. This four-dot system is the specific device geometry needed for two-qubit operations of a two-electron spin qubit. We extract the strength of the capacitive coupling between qubit and adjacent double quantum dot and show that the present geometry allows fast conditional gate operation, opening pathways toward implementation of a universal set of gates for singlet-triplet spin qubits.
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Affiliation(s)
- I van Weperen
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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37
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Nakaharai S, Williams JR, Marcus CM. Gate-defined graphene quantum point contact in the quantum Hall regime. Phys Rev Lett 2011; 107:036602. [PMID: 21838385 DOI: 10.1103/physrevlett.107.036602] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2010] [Indexed: 05/31/2023]
Abstract
We investigate transport in a gate-defined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of the sample and allowed to mix in this split-gate geometry. Among the expected quantum Hall features, an unexpected additional plateau at 0.5h/e2 is observed. We propose that chaotic mixing of edge channels gives rise to the extra plateau.
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Affiliation(s)
- S Nakaharai
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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38
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Williams JR, Low T, Lundstrom MS, Marcus CM. Gate-controlled guiding of electrons in graphene. Nat Nanotechnol 2011; 6:222-225. [PMID: 21317890 DOI: 10.1038/nnano.2011.3] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2010] [Accepted: 01/06/2011] [Indexed: 05/30/2023]
Abstract
Ballistic semiconductor structures have allowed the realization of optics-like phenomena in electronic systems, including the magnetic focusing and electrostatic lensing of electrons. An extension that appears unique to graphene is to use both n and p carrier types to create electronic analogues of optical devices with both positive and negative indices of refraction. Here, we use the gate-controlled density of both p and n carrier types in graphene to demonstrate the electronic analogue of fibre-optic guiding. Two basic effects are investigated: bipolar p-n junction guiding, based on the principle of angle-selective transmission through the interface between the graphene and the p-n junction; and unipolar fibre-optic guiding, using total internal reflection controlled by carrier density. We also demonstrate modulation of the guiding efficiency through gating, and comparison of these data with numerical simulations indicates that guiding performance is limited by the roughness of the interface. The development of p-n and fibre-optic guiding in graphene may lead to electrically reconfigurable wiring in high-mobility devices.
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Affiliation(s)
- J R Williams
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
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39
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Barthel C, Medford J, Marcus CM, Hanson MP, Gossard AC. Interlaced dynamical decoupling and coherent operation of a singlet-triplet qubit. Phys Rev Lett 2010; 105:266808. [PMID: 21231704 DOI: 10.1103/physrevlett.105.266808] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2010] [Indexed: 05/30/2023]
Abstract
We experimentally demonstrate coherence recovery of singlet-triplet superpositions by interlacing qubit rotations between Carr-Purcell (CP) echo sequences. We then compare the performance of Hahn, CP, concatenated dynamical decoupling (CDD), and Uhrig dynamical decoupling for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T(2)∼80 μs.
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Affiliation(s)
- C Barthel
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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40
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Kou A, McClure DT, Marcus CM, Pfeiffer LN, West KW. Dynamic nuclear polarization in the fractional quantum Hall regime. Phys Rev Lett 2010; 105:056804. [PMID: 20867946 DOI: 10.1103/physrevlett.105.056804] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2010] [Indexed: 05/29/2023]
Abstract
We investigate dynamic nuclear polarization in quantum point contacts (QPCs) in the integer and fractional quantum Hall regimes. Following the application of a dc bias, fractional plateaus in the QPC shift symmetrically about half filling of the lowest Landau level, ν=1/2, suggesting an interpretation in terms of composite fermions. Polarizing and detecting at different filling factors indicates that Zeeman energy is reduced by the induced nuclear polarization. Mapping effects from integer to fractional regimes extends the composite fermion picture to include hyperfine coupling.
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Affiliation(s)
- A Kou
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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41
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Reilly DJ, Taylor JM, Petta JR, Marcus CM, Hanson MP, Gossard AC. Exchange control of nuclear spin diffusion in a double quantum dot. Phys Rev Lett 2010; 104:236802. [PMID: 20867261 DOI: 10.1103/physrevlett.104.236802] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2009] [Indexed: 05/25/2023]
Abstract
The influence of gate-controlled two-electron exchange on the relaxation of nuclear polarization in small ensembles (N∼10(6)) of nuclear spins is examined in a GaAs double quantum dot system. Waiting in the (2,0) charge configuration, which has large exchange splitting, reduces the nuclear diffusion rate compared to that of the (1,1) configuration. Matching exchange to Zeeman splitting significantly increases the nuclear diffusion rate.
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Affiliation(s)
- D J Reilly
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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42
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Gullans M, Krich JJ, Taylor JM, Bluhm H, Halperin BI, Marcus CM, Stopa M, Yacoby A, Lukin MD. Dynamic nuclear polarization in double quantum dots. Phys Rev Lett 2010; 104:226807. [PMID: 20867197 DOI: 10.1103/physrevlett.104.226807] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2010] [Indexed: 05/29/2023]
Abstract
We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the buildup of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states", and the elimination of the difference field. We show that in the case of unequal dots, buildup of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, buildup of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process.
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Affiliation(s)
- M Gullans
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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43
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McClure DT, Zhang Y, Rosenow B, Levenson-Falk EM, Marcus CM, Pfeiffer LN, West KW. Edge-state velocity and coherence in a quantum Hall Fabry-Pérot interferometer. Phys Rev Lett 2009; 103:206806. [PMID: 20366002 DOI: 10.1103/physrevlett.103.206806] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2009] [Indexed: 05/29/2023]
Abstract
We investigate nonlinear transport in electronic Fabry-Pérot interferometers in the integer quantum Hall regime. For interferometers sufficiently large that Coulomb blockade effects are absent, a checkerboardlike pattern of conductance oscillations as a function of dc bias and perpendicular magnetic field is observed. Edge-state velocities extracted from the checkerboard data are compared to model calculations and found to be consistent with a crossover from skipping orbits at low fields to E-vector x B-vector drift at high fields. Suppression of visibility as a function of bias and magnetic field is accounted for by including energy- and field-dependent dephasing of edge electrons.
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Affiliation(s)
- D T McClure
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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44
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Abstract
We report nanoscale patterning of graphene using a helium ion microscope configured for lithography. Helium ion lithography is a direct-write lithography process, comparable to conventional focused ion beam patterning, with no resist or other material contacting the sample surface. In the present application, graphene samples on Si/SiO2 substrates are cut using helium ions, with computer controlled alignment, patterning, and exposure. Once suitable beam doses are determined, sharp edge profiles and clean etching are obtained, with little evident damage or doping to the sample. This technique provides fast lithography compatible with graphene, with approximately 15 nm feature sizes.
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Affiliation(s)
- D C Bell
- School of Engineering and Applied Sciences, Center for Nanoscale Systems, Harvard University, Cambridge, MA 02138, USA
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45
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Barthel C, Reilly DJ, Marcus CM, Hanson MP, Gossard AC. Rapid single-shot measurement of a singlet-triplet qubit. Phys Rev Lett 2009; 103:160503. [PMID: 19905680 DOI: 10.1103/physrevlett.103.160503] [Citation(s) in RCA: 78] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2009] [Indexed: 05/28/2023]
Abstract
We report repeated single-shot measurements of the two-electron spin state in a GaAs double quantum dot. The readout allows measurement with a fidelity above 90% with a approximately 7 micros cycle time. Hyperfine-induced precession between singlet and triplet states of the two-electron system are directly observed, as nuclear Overhauser fields are quasistatic on the time scale of the measurement cycle. Repeated measurements on millisecond to second time scales reveal the evolution of the nuclear environment.
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Affiliation(s)
- C Barthel
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
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46
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Churchill HOH, Kuemmeth F, Harlow JW, Bestwick AJ, Rashba EI, Flensberg K, Stwertka CH, Taychatanapat T, Watson SK, Marcus CM. Relaxation and dephasing in a two-electron 13C nanotube double quantum dot. Phys Rev Lett 2009; 102:166802. [PMID: 19518737 DOI: 10.1103/physrevlett.102.166802] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2008] [Indexed: 05/27/2023]
Abstract
We use charge sensing of Pauli blockade (including spin and isospin) in a two-electron 13C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time T1 first decreases with a parallel magnetic field and then goes through a minimum in a field of 1.4 T. We attribute both results to the spin-orbit-modified electronic spectrum of carbon nanotubes, which at high field enhances relaxation due to bending-mode phonons. The inhomogeneous dephasing time T{2} is consistent with previous data on hyperfine coupling strength in 13C nanotubes.
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Affiliation(s)
- H O H Churchill
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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47
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Reilly DJ, Taylor JM, Laird EA, Petta JR, Marcus CM, Hanson MP, Gossard AC. Measurement of temporal correlations of the overhauser field in a double quantum dot. Phys Rev Lett 2008; 101:236803. [PMID: 19113577 DOI: 10.1103/physrevlett.101.236803] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2007] [Indexed: 05/27/2023]
Abstract
In quantum dots made from materials with nonzero nuclear spins, hyperfine coupling creates a fluctuating effective Zeeman field (Overhauser field) felt by electrons, which can be a dominant source of spin qubit decoherence. We characterize the spectral properties of the fluctuating Overhauser field in a GaAs double quantum dot by measuring correlation functions and power spectra of the rate of singlet-triplet mixing of two separated electrons. Away from zero field, spectral weight is concentrated below 10 Hz, with approximately 1/f2 dependence on frequency f. This is consistent with a model of nuclear spin diffusion, and indicates that decoherence can be largely suppressed by echo techniques.
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Affiliation(s)
- D J Reilly
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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48
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Abstract
Coherent spin states in semiconductor quantum dots offer promise as electrically controllable quantum bits (qubits) with scalable fabrication. For few-electron quantum dots made from gallium arsenide (GaAs), fluctuating nuclear spins in the host lattice are the dominant source of spin decoherence. We report a method of preparing the nuclear spin environment that suppresses the relevant component of nuclear spin fluctuations below its equilibrium value by a factor of approximately 70, extending the inhomogeneous dephasing time for the two-electron spin state beyond 1 microsecond. The nuclear state can be readily prepared by electrical gate manipulation and persists for more than 10 seconds.
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Affiliation(s)
- D J Reilly
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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49
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Abstract
We employ density functional calculated eigenstates as a basis for exact diagonalization studies of semiconductor double quantum dots, with two electrons, through the transition from the symmetric bias regime to the regime where both electrons occupy the same dot. We calculate the singlet-triplet splitting J(epsilon) as a function of bias detuning epsilon and explain its functional shape with a simple, double anticrossing model. A voltage noise suppression "sweet spot," where d J(epsilon)/d(epsilon) = 0 with nonzero J(epsilon), is predicted and shown to be tunable with a magnetic field B.
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Affiliation(s)
- M Stopa
- Center for Nanoscale Systems, and Department of Physics, Harvard University, Cambridge, MA 02138, USA.
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50
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Radu IP, Miller JB, Marcus CM, Kastner MA, Pfeiffer LN, West KW. Quasi-Particle Properties from Tunneling in the
v
= 5/2 Fractional Quantum Hall State. Science 2008; 320:899-902. [DOI: 10.1126/science.1157560] [Citation(s) in RCA: 267] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Iuliana P. Radu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - J. B. Miller
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - C. M. Marcus
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - M. A. Kastner
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - L. N. Pfeiffer
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
| | - K. W. West
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Bell Laboratories, Alcatel-Lucent Technologies, Murray Hill, NJ 07974, USA
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