1
|
Ungerer JH, Pally A, Kononov A, Lehmann S, Ridderbos J, Potts PP, Thelander C, Dick KA, Maisi VF, Scarlino P, Baumgartner A, Schönenberger C. Strong coupling between a microwave photon and a singlet-triplet qubit. Nat Commun 2024; 15:1068. [PMID: 38316779 PMCID: PMC10844229 DOI: 10.1038/s41467-024-45235-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Accepted: 01/18/2024] [Indexed: 02/07/2024] Open
Abstract
Combining superconducting resonators and quantum dots has triggered tremendous progress in quantum information, however, attempts at coupling a resonator to even charge parity spin qubits have resulted only in weak spin-photon coupling. Here, we integrate a zincblende InAs nanowire double quantum dot with strong spin-orbit interaction in a magnetic-field resilient, high-quality resonator. The quantum confinement in the nanowire is achieved using deterministically grown wurtzite tunnel barriers. Our experiments on even charge parity states and at large magnetic fields, allow us to identify the relevant spin states and to measure the spin decoherence rates and spin-photon coupling strengths. We find an anti-crossing between the resonator mode in the single photon limit and a singlet-triplet qubit with a spin-photon coupling strength of g/2π = 139 ± 4 MHz. This coherent coupling exceeds the resonator decay rate κ/2π = 19.8 ± 0.2 MHz and the qubit dephasing rate γ/2π = 116 ± 7 MHz, putting our system in the strong coupling regime.
Collapse
Affiliation(s)
- J H Ungerer
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland.
- Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland.
| | - A Pally
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland.
| | - A Kononov
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - S Lehmann
- Solid State Physics and NanoLund, Lund University, Box 118, S-22100, Lund, Sweden
| | - J Ridderbos
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands
| | - P P Potts
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
- Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - C Thelander
- Solid State Physics and NanoLund, Lund University, Box 118, S-22100, Lund, Sweden
| | - K A Dick
- Centre for Analysis and Synthesis, Lund University, Box 124, S-22100, Lund, Sweden
| | - V F Maisi
- Solid State Physics and NanoLund, Lund University, Box 118, S-22100, Lund, Sweden
| | - P Scarlino
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
| | - A Baumgartner
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
- Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - C Schönenberger
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
- Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| |
Collapse
|
2
|
van Driel D, Wang G, Bordin A, van Loo N, Zatelli F, Mazur GP, Xu D, Gazibegovic S, Badawy G, Bakkers EPAM, Kouwenhoven LP, Dvir T. Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices. Nat Commun 2023; 14:6880. [PMID: 37898657 PMCID: PMC10613242 DOI: 10.1038/s41467-023-42026-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 09/27/2023] [Indexed: 10/30/2023] Open
Abstract
Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.
Collapse
Affiliation(s)
- David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Francesco Zatelli
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Di Xu
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands.
| |
Collapse
|
3
|
Levajac V, Wang JY, Sfiligoj C, Lemang M, Wolff JC, Bordin A, Badawy G, Gazibegovic S, Bakkers EPAM, Kouwenhoven LP. Subgap spectroscopy along hybrid nanowires by nm-thick tunnel barriers. Nat Commun 2023; 14:6647. [PMID: 37863952 PMCID: PMC10589238 DOI: 10.1038/s41467-023-42422-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 10/11/2023] [Indexed: 10/22/2023] Open
Abstract
Tunneling spectroscopy is widely used to examine the subgap spectra in semiconductor-superconductor nanostructures when searching for Majorana zero modes (MZMs). Typically, semiconductor sections controlled by local gates at the ends of hybrids serve as tunnel barriers. Besides detecting states only at the hybrid ends, such gate-defined tunnel probes can cause the formation of non-topological subgap states that mimic MZMs. Here, we develop an alternative type of tunnel probes to overcome these limitations. After the growth of an InSb-Al hybrid nanowire, a precisely controlled in-situ oxidation of the Al shell is performed to yield a nm-thick AlOx layer. In such thin isolating layer, tunnel probes can be arbitrarily defined at any position along the hybrid nanowire by shadow-wall angle-deposition of metallic leads. In this work, we make multiple tunnel probes along single nanowire hybrids and successfully identify Andreev bound states (ABSs) of various spatial extension residing along the hybrids.
Collapse
Affiliation(s)
- Vukan Levajac
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands.
- Beijing Academy of Quantum Information Sciences, 100193, Beijing, China.
| | - Cristina Sfiligoj
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Mathilde Lemang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Jan Cornelis Wolff
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| |
Collapse
|
4
|
Hess R, Legg HF, Loss D, Klinovaja J. Trivial Andreev Band Mimicking Topological Bulk Gap Reopening in the Nonlocal Conductance of Long Rashba Nanowires. PHYSICAL REVIEW LETTERS 2023; 130:207001. [PMID: 37267549 DOI: 10.1103/physrevlett.130.207001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 02/07/2023] [Accepted: 04/04/2023] [Indexed: 06/04/2023]
Abstract
We consider a one-dimensional Rashba nanowire in which multiple Andreev bound states in the bulk of the nanowire form an Andreev band. We show that, under certain circumstances, this trivial Andreev band can produce an apparent closing and reopening signature of the bulk band gap in the nonlocal conductance of the nanowire. Furthermore, we show that the existence of the trivial bulk reopening signature in nonlocal conductance is essentially unaffected by the additional presence of trivial zero-bias peaks in the local conductance at either end of the nanowire. The simultaneous occurrence of a trivial bulk reopening signature and zero-bias peaks mimics the basic features required to pass the so-called "topological gap protocol." Our results therefore provide a topologically trivial minimal model by which the applicability of this protocol can be benchmarked.
Collapse
Affiliation(s)
- Richard Hess
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Henry F Legg
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Daniel Loss
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Jelena Klinovaja
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| |
Collapse
|
5
|
Potts H, Aspegren M, Debbarma R, Lehmann S, Thelander C. Large-bias spectroscopy of Yu-Shiba-Rusinov states in a double quantum dot. NANOTECHNOLOGY 2023; 34:135002. [PMID: 36595334 DOI: 10.1088/1361-6528/aca90e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 12/05/2022] [Indexed: 06/17/2023]
Abstract
We have performed tunnel transport spectroscopy on a quantum dot (QD) molecule proximitized by a superconducting contact. In such a system, the scattering between QD spins and Bogoliubov quasiparticles leads to the formation of Yu-Shiba-Rusinov (YSR) states within the superconducting gap. In this work, we investigate interactions appearing when one- and two-electron spin states in a double-QD energetically align with the superconducting gap edge. We find that the inter-dot spin-triplet state interacts considerably stronger with the superconductor than the corresponding singlet, pointing to stronger screening. By forming a ring molecule with a significant orbital contribution to the effectiveg-factor, we observe interactions of all four spin-orbital one-electron states with the superconductor under a weak magnetic field.
Collapse
Affiliation(s)
- Heidi Potts
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| | - Markus Aspegren
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| | - Rousan Debbarma
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| | - Sebastian Lehmann
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| | - Claes Thelander
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| |
Collapse
|
6
|
Bordoloi A, Zannier V, Sorba L, Schönenberger C, Baumgartner A. Spin cross-correlation experiments in an electron entangler. Nature 2022; 612:454-458. [PMID: 36424409 DOI: 10.1038/s41586-022-05436-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Accepted: 10/10/2022] [Indexed: 11/27/2022]
Abstract
Correlations are fundamental in describing many-body systems. However, in experiments, correlations are notoriously difficult to assess on a microscopic scale, especially for electron spins. Even though it is firmly established theoretically that the electrons in a Cooper pair1 of a superconductor form maximally spin-entangled singlet states with opposite spin projections2-4, no spin correlation experiments have been demonstrated so far. Here we report the direct measurement of the spin cross-correlations between the currents of a Cooper pair splitter5-13, an electronic device that emits electrons originating from Cooper pairs. We use ferromagnetic split-gates14,15, compatible with nearby superconducting structures, to individually spin polarize the transmissions of the quantum dots in the two electronic paths, which act as tunable spin filters. The signals are detected in standard transport and in highly sensitive transconductance experiments. We find that the spin cross-correlation is negative, consistent with spin singlet emission, and deviates from the ideal value mostly due to the overlap of the Zeeman split quantum dot states. Our results demonstrate a new route to perform spin correlation experiments in nano-electronic devices, especially suitable for those relying on magnetic field sensitive superconducting elements, like triplet or topologically non-trivial superconductors16-18, or to perform Bell tests with massive particles19,20.
Collapse
Affiliation(s)
- Arunav Bordoloi
- Department of Physics, University of Basel, Basel, Switzerland. .,Department of Physics, University of Maryland, College Park, MD, USA.
| | - Valentina Zannier
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - Lucia Sorba
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - Christian Schönenberger
- Department of Physics, University of Basel, Basel, Switzerland.,Swiss Nanoscience Institute, University of Basel, Basel, Switzerland
| | - Andreas Baumgartner
- Department of Physics, University of Basel, Basel, Switzerland. .,Swiss Nanoscience Institute, University of Basel, Basel, Switzerland.
| |
Collapse
|
7
|
Marra P, Nigro A. Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:124001. [PMID: 34929683 DOI: 10.1088/1361-648x/ac44d2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2021] [Accepted: 12/20/2021] [Indexed: 06/14/2023]
Abstract
Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.
Collapse
Affiliation(s)
- Pasquale Marra
- Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
- Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan
| | - Angela Nigro
- Dipartimento di Fisica 'E. R. Caianiello', Università degli Studi di Salerno, 84084 Fisciano (Salerno), Italy
- Consiglio Nazionale delle Ricerche CNR-SPIN, UOS Salerno, 84084 Fisciano (Salerno), Italy
| |
Collapse
|
8
|
Valentini M, Peñaranda F, Hofmann A, Brauns M, Hauschild R, Krogstrup P, San-Jose P, Prada E, Aguado R, Katsaros G. Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states. Science 2021; 373:82-88. [PMID: 34210881 DOI: 10.1126/science.abf1513] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 05/21/2021] [Indexed: 11/02/2022]
Abstract
A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magnetic field dependence of the Andreev levels, through both the Zeeman and Little-Parks effects, may result in robust zero-bias peaks-features that could be easily misinterpreted as originating from Majorana zero modes but are unrelated to topological superconductivity.
Collapse
Affiliation(s)
- Marco Valentini
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
| | - Fernando Peñaranda
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Andrea Hofmann
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Matthias Brauns
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Robert Hauschild
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Peter Krogstrup
- Microsoft Quantum Materials Lab and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Kanalvej 7, 2800 Kongens Lyngby, Denmark
| | - Pablo San-Jose
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Elsa Prada
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain.,Departamento de Física de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Ramón Aguado
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain.
| | - Georgios Katsaros
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
| |
Collapse
|
9
|
Gong T, Dai XF, Zhang LL, Jiang C, Gong WJ. Interference effect on the Andreev reflections induced by Majorana bound states. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:215303. [PMID: 33588382 DOI: 10.1088/1361-648x/abe651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Accepted: 02/15/2021] [Indexed: 06/12/2023]
Abstract
We investigate the effect of quantum interference on the Andreev reflections (ARs) induced by Majorana bound states (MBSs), by considering their additional coupling via a quantum-dot molecule. It is found that due to the direct and indirect couplings of MBSs, a quantum ring is constructed in this system. Consequently, the interference effect makes important contribution to the ARs, especially in the presence of the local magnetic flux. All the results are manifested as the tight dependence of the differential conductance and Fano factors on the magnetic flux phase factor, dot-MBS couplings, and the dot level, respectively. Moreover, at the zero-bias limit, the magnitudes of the Fano factors and their relation can be efficiently altered by the interference properties. We believe that quantum interference is important for manipulating the Andreev reflection behaviors of the MBSs.
Collapse
Affiliation(s)
- Tong Gong
- College of Sciences, Northeastern University, Shenyang 110819, People's Republic of China
| | - Xue-Feng Dai
- College of Sciences, Northeastern University, Shenyang 110819, People's Republic of China
| | - Lian-Lian Zhang
- College of Sciences, Northeastern University, Shenyang 110819, People's Republic of China
| | - Cui Jiang
- Basic Department, Shenyang Institute of Engineering, Shenyang, 110136, People's Republic of China
| | - Wei-Jiang Gong
- College of Sciences, Northeastern University, Shenyang 110819, People's Republic of China
| |
Collapse
|