1
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Huang SM, Lin C, You SY, Yan YJ, Yu SH, Chou M. The quantum oscillations in different probe configurations in the [Formula: see text] topological insulator macroflake. Sci Rep 2022; 12:5191. [PMID: 35338190 PMCID: PMC8956641 DOI: 10.1038/s41598-022-09073-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 03/10/2022] [Indexed: 11/08/2022] Open
Abstract
We demonstrate quantum oscillations in [Formula: see text] topological insulator macroflakes in different probe configurations. The oscillation period in the local configuration is twice compared to the non-local configuration. The Aharonov-Bohm-like (AB-like) oscillation dominates the transport property in the local configuration and the Altshuler-Aronov-Spivak-like (AAS-like) oscillation dominates the transport property in the non-local configuration. The AB-like oscillation period is 0.21 T and the related loop diameter is 156 nm which is consistent with the reported phase coherence length in topological insulators. The Shubnikov-de Haas oscillation frequency is the same but oscillation peaks reveal a [Formula: see text] phase shift in the local and non-local configuration. The Berry phase is [Formula: see text] in the local configuration and 0 in non-local configuration.
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Affiliation(s)
- Shiu-Ming Huang
- Department of Physics, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
- Center of Crystal Research, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
- Taiwan Consortium of Emergent Crystalline Materials, TCECM, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Chien Lin
- Department of Physics, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Sheng-Yu You
- Department of Physics, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - You-Jhih Yan
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Shih-Hsun Yu
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Mitch Chou
- Center of Crystal Research, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
- Taiwan Consortium of Emergent Crystalline Materials, TCECM, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
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2
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Strambini E, Iorio A, Durante O, Citro R, Sanz-Fernández C, Guarcello C, Tokatly IV, Braggio A, Rocci M, Ligato N, Zannier V, Sorba L, Bergeret FS, Giazotto F. A Josephson phase battery. NATURE NANOTECHNOLOGY 2020; 15:656-660. [PMID: 32541945 DOI: 10.1038/s41565-020-0712-7] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2020] [Accepted: 05/12/2020] [Indexed: 06/11/2023]
Abstract
A classical battery converts chemical energy into a persistent voltage bias that can power electronic circuits. Similarly, a phase battery is a quantum device that provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on phase coherence. Here we demonstrate a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states, that is proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias φ0 across the wire, leading to the anomalous Josephson effect1,2. We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ0. Hence, we can charge and discharge the quantum phase battery. The observed symmetries of the anomalous Josephson effect in the vectorial magnetic field are in agreement with our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction induces a strong coupling between charge, spin and superconducting phase, able to break the phase rigidity of the system.
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Affiliation(s)
- Elia Strambini
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy.
| | - Andrea Iorio
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy.
| | - Ofelia Durante
- Dipartimento di Fisica 'E. R. Caianiello', Università di Salerno, Fisciano, Italy
| | - Roberta Citro
- Dipartimento di Fisica 'E. R. Caianiello', Università di Salerno, Fisciano, Italy
| | | | - Claudio Guarcello
- Dipartimento di Fisica 'E. R. Caianiello', Università di Salerno, Fisciano, Italy
- Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, San Sebastián, Spain
| | - Ilya V Tokatly
- Nano-Bio Spectroscopy Group, Departamento de Física de Materiales, Universidad del País Vasco (UPV/EHU), Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, Bilbao, Spain
| | - Alessandro Braggio
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - Mirko Rocci
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
- Francis Bitter Magnet Laboratory and Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Nadia Ligato
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - Valentina Zannier
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - Lucia Sorba
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - F Sebastián Bergeret
- Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, San Sebastián, Spain.
- Donostia International Physics Center (DIPC), San Sebastián, Spain.
| | - Francesco Giazotto
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy.
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3
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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] [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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4
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How to measure the entropy of a mesoscopic system via thermoelectric transport. Nat Commun 2019; 10:5801. [PMID: 31862879 PMCID: PMC6925120 DOI: 10.1038/s41467-019-13630-3] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Accepted: 11/12/2019] [Indexed: 11/08/2022] Open
Abstract
Entropy is a fundamental thermodynamic quantity indicative of the accessible degrees of freedom in a system. While it has been suggested that the entropy of a mesoscopic system can yield nontrivial information on emergence of exotic states, its measurement in such small electron-number system is a daunting task. Here we propose a method to extract the entropy of a Coulomb-blockaded mesoscopic system from transport measurements. We prove analytically and demonstrate numerically the applicability of the method to such a mesoscopic system of arbitrary spectrum and degeneracies. We then apply our procedure to measurements of thermoelectric response of a single quantum dot, and demonstrate how it can be used to deduce the entropy change across Coulomb-blockade valleys, resolving, along the way, a long-standing puzzle of the experimentally observed finite thermoelectric response at the apparent particle-hole symmetric point.
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5
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Bäuerle C, Christian Glattli D, Meunier T, Portier F, Roche P, Roulleau P, Takada S, Waintal X. Coherent control of single electrons: a review of current progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:056503. [PMID: 29355831 DOI: 10.1088/1361-6633/aaa98a] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.
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Affiliation(s)
- Christopher Bäuerle
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
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6
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Jauregui LA, Pettes MT, Rokhinson LP, Shi L, Chen YP. Magnetic field-induced helical mode and topological transitions in a topological insulator nanoribbon. NATURE NANOTECHNOLOGY 2016; 11:345-351. [PMID: 26780658 DOI: 10.1038/nnano.2015.293] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2015] [Accepted: 11/12/2015] [Indexed: 06/05/2023]
Abstract
The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.
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Affiliation(s)
- Luis A Jauregui
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Michael T Pettes
- Department of Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| | - Leonid P Rokhinson
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Li Shi
- Department of Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
- Materials Science and Engineering Program, University of Texas at Austin, Austin, Texas 78712, USA
| | - Yong P Chen
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
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7
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Takada S, Bäuerle C, Yamamoto M, Watanabe K, Hermelin S, Meunier T, Alex A, Weichselbaum A, von Delft J, Ludwig A, Wieck AD, Tarucha S. Transmission phase in the Kondo regime revealed in a two-path interferometer. PHYSICAL REVIEW LETTERS 2014; 113:126601. [PMID: 25279636 DOI: 10.1103/physrevlett.113.126601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2013] [Indexed: 06/03/2023]
Abstract
We report on the direct observation of the transmission phase shift through a Kondo correlated quantum dot by employing a new type of two-path interferometer. We observed a clear π/2-phase shift, which persists up to the Kondo temperature TK. Above this temperature, the phase shifts by more than π/2 at each Coulomb peak, approaching the behavior observed for the standard Coulomb blockade regime. These observations are in remarkable agreement with two-level numerical renormalization group calculations. The unique combination of experimental and theoretical results presented here fully elucidates the phase evolution in the Kondo regime.
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Affiliation(s)
- S Takada
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - C Bäuerle
- Université Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France and CNRS, Institut NEEL, F-38042 Grenoble, France
| | - M Yamamoto
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan and PRESTO, JST, Kawaguchi-shi, Saitama 331-0012, Japan
| | - K Watanabe
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - S Hermelin
- Université Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France and CNRS, Institut NEEL, F-38042 Grenoble, France
| | - T Meunier
- Université Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France and CNRS, Institut NEEL, F-38042 Grenoble, France
| | - A Alex
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 München, Germany
| | - A Weichselbaum
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 München, Germany
| | - J von Delft
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 München, Germany
| | - A Ludwig
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany
| | - A D Wieck
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany
| | - S Tarucha
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan and RIKEN Center for Emergent Matter Science (CEMS), 2-1 Hirosawa, Wako-shi, Saitama 31-0198, Japan
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8
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Sawant R, Samuel J, Sinha A, Sinha S, Sinha U. Nonclassical paths in quantum interference experiments. PHYSICAL REVIEW LETTERS 2014; 113:120406. [PMID: 25279612 DOI: 10.1103/physrevlett.113.120406] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2013] [Indexed: 06/03/2023]
Abstract
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
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Affiliation(s)
- Rahul Sawant
- Raman Research Institute, Sadashivanagar, Bangalore 560 080, India
| | - Joseph Samuel
- Raman Research Institute, Sadashivanagar, Bangalore 560 080, India
| | - Aninda Sinha
- Centre for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India
| | - Supurna Sinha
- Raman Research Institute, Sadashivanagar, Bangalore 560 080, India
| | - Urbasi Sinha
- Raman Research Institute, Sadashivanagar, Bangalore 560 080, India and Institute for Quantum Computing, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
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9
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Gong WJ, Han Y, Wei GZ, Du A. Spin accumulation assisted by the Aharonov-Bohm-Fano effect of quantum dot structures. NANOSCALE RESEARCH LETTERS 2012; 7:510. [PMID: 22985404 PMCID: PMC3564718 DOI: 10.1186/1556-276x-7-510] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/11/2012] [Accepted: 07/20/2012] [Indexed: 06/01/2023]
Abstract
: We investigate the spin accumulations of Aharonov-Bohm interferometers with embedded quantum dots by considering spin bias in the leads. It is found that regardless of the interferometer configurations, the spin accumulations are closely determined by their quantum interference features. This is mainly manifested in the dependence of spin accumulations on the threaded magnetic flux and the nonresonant transmission process. Namely, the Aharonov-Bohm-Fano effect is a necessary condition to achieve the spin accumulation in the quantum dot of the resonant channel. Further analysis showed that in the double-dot interferometer, the spin accumulation can be detailedly manipulated. The spin accumulation properties of such structures offer a new scheme of spin manipulation. When the intradot Coulomb interactions are taken into account, we find that the electron interactions are advantageous to the spin accumulation in the resonant channel.
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Affiliation(s)
- Wei-Jiang Gong
- College of Sciences, Northeastern University, Shenyang, 110819, China
- International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang, 110016, China
| | - Yu Han
- Department of Physics, Liaoning University, Shenyang, 110036, China
| | - Guo-Zhu Wei
- College of Sciences, Northeastern University, Shenyang, 110819, China
- International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang, 110016, China
| | - An Du
- College of Sciences, Northeastern University, Shenyang, 110819, China
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10
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Kretinin AV, Chung Y. Wide-band current preamplifier for conductance measurements with large input capacitance. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2012; 83:084704. [PMID: 22938321 DOI: 10.1063/1.4740521] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
A wide-band current preamplifier based on a composite operational amplifier is proposed. It has been shown that the bandwidth of the preamplifier can be significantly increased by enhancing the effective open-loop gain. The described 10(7) V/A current gain preamplifier had the bandwidth of about 100 kHz with the 1 nF input shunt capacitance. The measured preamplifier current noise was 46 fA/√Hz at 1 kHz, close to the design noise minimum. The voltage noise was found to be about 2.9 nV/√Hz at 1 kHz, which is in a good agreement with the value expected for the particular operational amplifier used in the input stage. By analysing the total produced noise we found that the optimal frequency range suitable for the fast lock-in measurements is from 1 kHz to 2 kHz. To obtain the same signal-to-noise ratio, the reported preamplifier requires ~10% of the integration time needed in measurements made with a conventional preamplifier.
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Affiliation(s)
- Andrey V Kretinin
- Condensed Matter Physics Department, Weizmann Institute of Science, Rehovot, Israel
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11
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Yamamoto M, Takada S, Bäuerle C, Watanabe K, Wieck AD, Tarucha S. Electrical control of a solid-state flying qubit. NATURE NANOTECHNOLOGY 2012; 7:247-251. [PMID: 22426515 DOI: 10.1038/nnano.2012.28] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2011] [Accepted: 02/13/2012] [Indexed: 05/31/2023]
Abstract
Solid-state approaches to quantum information technology are attractive because they are scalable. The coherent transport of quantum information over large distances is a requirement for any practical quantum computer and has been demonstrated by coupling super-conducting qubits to photons. Single electrons have also been transferred between distant quantum dots in times shorter than their spin coherence time. However, until now, there have been no demonstrations of scalable 'flying qubit' architectures-systems in which it is possible to perform quantum operations on qubits while they are being coherently transferred-in solid-state systems. These architectures allow for control over qubit separation and for non-local entanglement, which makes them more amenable to integration and scaling than static qubit approaches. Here, we report the transport and manipulation of qubits over distances of 6 µm within 40 ps, in an Aharonov-Bohm ring connected to two-channel wires that have a tunable tunnel coupling between channels. The flying qubit state is defined by the presence of a travelling electron in either channel of the wire, and can be controlled without a magnetic field. Our device has shorter quantum gates (<1 µm), longer coherence lengths (∼86 µm at 70 mK) and higher operating frequencies (∼100 GHz) than other solid-state implementations of flying qubits.
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Affiliation(s)
- Michihisa Yamamoto
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo, 113-8656, Japan.
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12
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Puller VI, Meir Y. How to measure the transmission phase through a quantum dot in a two-terminal interferometer. PHYSICAL REVIEW LETTERS 2010; 104:256801. [PMID: 20867406 DOI: 10.1103/physrevlett.104.256801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2010] [Indexed: 05/29/2023]
Abstract
Measurement of the transmission phase through a quantum dot (QD) embedded in an arm of a two-terminal Aharonov-Bohm (AB) interferometer is inhibited by phase symmetry, i.e., the property that the linear response conductance of a two-terminal device is an even function of the magnetic field. It is demonstrated that in a setup consisting of an interferometer with a QD in each of its arms, with one of the QDs capacitively coupled to a nearby quantum point contact (QPC), phase symmetry is broken when a finite voltage bias is applied to the QPC. The transmission phase via the uncoupled QD can then be deduced from the amplitude of the odd component of the AB oscillations.
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Affiliation(s)
- Vadim I Puller
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
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13
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Hernández AR, Lewenkopf CH. Nonlinear conductance in a ballistic Aharonov-Bohm ring. PHYSICAL REVIEW LETTERS 2009; 103:166801. [PMID: 19905714 DOI: 10.1103/physrevlett.103.166801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2009] [Indexed: 05/28/2023]
Abstract
The nonlinear electronic transport properties of a ballistic Aharonov-Bohm ring are investigated. It is demonstrated how the electronic interaction breaks the phase rigidity in a two-probe mesoscopic device as the voltage bias is increased. The possibility of studying interference effects in the nonlinear regime is addressed. The occurrence of magnetic field symmetries in higher order conductance coefficients is analyzed. The results are compared with recent experimental data.
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Affiliation(s)
- Alexis R Hernández
- Laboratório Nacional de Luz Síncrotron, Caixa Postal 6192, 13084-971 Campinas, Brazil
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14
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Hedin ER, Joe YS, Satanin AM. Resonance and phase shift in an open Aharonov-Bohm ring with an embedded quantum dot. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:015303. [PMID: 21817218 DOI: 10.1088/0953-8984/21/1/015303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The transmission and phase properties of electron transport through a quantum dot (QD) with variable coupling to a third-terminal probe are investigated analytically for the case of the QD connected directly to source and drain reservoirs and when the QD is embedded in one arm of an Aharonov-Bohm (AB) ring. Using the tight-binding model, explicit analytical expressions of the transmission through the QD for each case are given. Expressions for the conductance with coupling to the third terminal, which breaks unitarity and phase-locking, are also given. It is shown that in a three-terminal interferometer the zero of the Fano resonance in the transmission moves off the real energy axis for finite values of the coupling parameter. The zero orbits around the pole in the complex energy plane as a function of magnetic flux through the ring, and can be returned to the real energy axis unless the coupling parameter exceeds a critical value. With the QD embedded in one arm of the AB ring, the electron transmission and the transmission phase, and the phase of the AB oscillations, are described in relation to the degree of coupling to the third-terminal probe which opens the interferometer. By tuning the degree of coupling to the probe, it is shown that the phase of the AB oscillations can be made to match the intrinsic phase of the QD, facilitating experimental characterization of the phase response of the QD.
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Affiliation(s)
- Eric R Hedin
- Center for Computational Nanoscience, Department of Physics and Astronomy, Ball State University, Muncie, IN 47306, USA
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Neder I, Ginossar E. Behavior of electronic interferometers in the nonlinear regime. PHYSICAL REVIEW LETTERS 2008; 100:196806. [PMID: 18518476 DOI: 10.1103/physrevlett.100.196806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2007] [Indexed: 05/26/2023]
Abstract
We investigate theoretically the behavior of the current oscillations in an electronic Mach-Zehnder interferometer (MZI) as a function of its source bias. Recently, the MZI visibility data showed an unexplained lobe pattern with a peculiar phase rigidity. Moreover, the effect did not depend on the MZI path length difference. We argue that these effects may be a new many-body manifestation of particle-wave duality in quantum mechanics. When biasing the interferometer sources so much that multiple electrons are on each arm at any instant in time, quantum shot noise (a particle phenomena) must affect the interference pattern of the electrons that create it. A solution to the interaction Hamiltonian presented here shows that the interference visibility has a lobe pattern with applied bias that has a period proportional to the average path length and independent of the path length difference, together with a phase rigidity.
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Affiliation(s)
- I Neder
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot, Israel.
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Leturcq R, Sánchez D, Götz G, Ihn T, Ensslin K, Driscoll DC, Gossard AC. Magnetic field symmetry and phase rigidity of the nonlinear conductance in a ring. PHYSICAL REVIEW LETTERS 2006; 96:126801. [PMID: 16605938 DOI: 10.1103/physrevlett.96.126801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2005] [Indexed: 05/08/2023]
Abstract
We have performed nonlinear transport measurements as a function of a perpendicular magnetic field in a semiconductor Aharonov-Bohm ring connected to two leads. While the voltage-symmetric part of the conductance is symmetric in the magnetic field, the voltage-antisymmetric part of the conductance is not symmetric. These symmetry relations are compatible with the scattering theory for nonlinear mesoscopic transport. The observed asymmetry can be tuned continuously by changing the gate voltages near the arms of the ring, showing that the phase of the nonlinear conductance in a two-terminal interferometer is not rigid, in contrast with the case for the linear conductance.
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Affiliation(s)
- R Leturcq
- Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland.
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Neder I, Heiblum M, Levinson Y, Mahalu D, Umansky V. Unexpected behavior in a two-path electron interferometer. PHYSICAL REVIEW LETTERS 2006; 96:016804. [PMID: 16486497 DOI: 10.1103/physrevlett.96.016804] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2005] [Indexed: 05/06/2023]
Abstract
We report the observation of an unpredictable behavior of a simple, two-path, electron interferometer. Utilizing an electronic analog of the well-known optical Mach-Zehnder interferometer, with current carrying edge channels in the quantum Hall effect regime, we measured high contrast Aharonov-Bohm (AB) oscillations. Surprisingly, the amplitude of the oscillations varied with energy in a lobe fashion, namely, with distinct maxima and zeros (namely, no AB oscillations) in between. Moreover, the phase of the AB oscillations was constant throughout each lobe period but slipped abruptly by pi at each zero. The periodicity of the lobes defines a new energy scale, which may be a general characteristic of quantum coherence of interfering electrons.
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Affiliation(s)
- I Neder
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Avinun-Kalish M, Heiblum M, Zarchin O, Mahalu D, Umansky V. Crossover from ‘mesoscopic’ to ‘universal’ phase for electron transmission in quantum dots. Nature 2005; 436:529-33. [PMID: 16049482 DOI: 10.1038/nature03899] [Citation(s) in RCA: 137] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2005] [Accepted: 06/08/2005] [Indexed: 11/08/2022]
Abstract
The measurement of phase in coherent electron systems--that is, 'mesoscopic' systems such as quantum dots--can yield information about fundamental transport properties that is not readily apparent from conductance measurements. Phase measurements on relatively large quantum dots recently revealed that the phase evolution for electrons traversing the dots exhibits a 'universal' behaviour, independent of dot size, shape, and electron occupancy. Specifically, for quantum dots in the Coulomb blockade regime, the transmission phase increases monotonically by pi throughout each conductance peak; in the conductance valleys, the phase returns sharply to its starting value. The expected mesoscopic features in the phase evolution--related to the dot's shape, spin degeneracy or to exchange effects--have not been observed, and there is at present no satisfactory explanation for the observed universality in phase behaviour. Here we report the results of phase measurements on a series of small quantum dots, having occupancies of between only 1-20 electrons, where the phase behaviour for electron transmission should in principle be easier to interpret. In contrast to the universal behaviour observed thus far only in the larger dots, we see clear mesoscopic features in the phase measurements when the dot occupancy is less than approximately 10 electrons. As the occupancy increases, the manner of phase evolution changes and universal behaviour is recovered for some 14 electrons or more. The identification of a transition from the expected mesoscopic behaviour to universal phase evolution should help to direct and constrain theoretical models for the latter.
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Affiliation(s)
- M Avinun-Kalish
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Aikawa H, Kobayashi K, Sano A, Katsumoto S, Iye Y. Observation of "partial coherence" in an Aharonov-Bohm interferometer with a quantum dot. PHYSICAL REVIEW LETTERS 2004; 92:176802. [PMID: 15169178 DOI: 10.1103/physrevlett.92.176802] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2003] [Indexed: 05/24/2023]
Abstract
We report experiments on the interference through spin states of electrons in a quantum dot (QD) embedded in an Aharonov-Bohm (AB) interferometer. We have picked up a spin-pair state, for which the environmental conditions are ideally similar. The AB amplitude is traced in a range of gate voltage that covers the pair. The behavior of the asymmetry in the amplitude around the two Coulomb peaks agrees with the theoretical prediction that the spin-flip process in a QD is related to the quantum dephasing of electrons. These results constitute evidence of "partial coherence" due to an entanglement of spins in the QD and in the interferometer.
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Affiliation(s)
- Hisashi Aikawa
- Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Chiba 277-8581, Japan
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Gerland U, Costi TA, Oreg Y. Transmission phase shift of a quantum dot with kondo correlations. PHYSICAL REVIEW LETTERS 2000; 84:3710-3713. [PMID: 11019183 DOI: 10.1103/physrevlett.84.3710] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/1999] [Indexed: 05/23/2023]
Abstract
We study the effects of Kondo correlations on the transmission phase shift of a quantum dot in an Aharonov-Bohm ring. We predict in detail how the development of a Kondo resonance should affect the dependence of the phase shift on transport voltage, gate voltage, and temperature. This system should allow the first direct observation of the well-known scattering phase shift of pi/2 expected (but not directly measurable in bulk systems) at zero temperature for an electron scattering off a spin- 1 / 2 impurity that is screened into a singlet.
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Affiliation(s)
- U Gerland
- Institut fur Theoretische Festkorperphysik, Universitat Karlsruhe, 76128 Karlsruhe, Germany
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Schuster R, Buks E, Heiblum M, Mahalu D, Umansky V, Shtrikman H. Phase measurement in a quantum dot via a double-slit interference experiment. Nature 1997. [DOI: 10.1038/385417a0] [Citation(s) in RCA: 507] [Impact Index Per Article: 18.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Buks E, Schuster R, Heiblum M, Mahalu D, Umansky V, Shtrikman H. Measurement of Phase and Magnitude of the Reflection Coefficient of a Quantum Dot. PHYSICAL REVIEW LETTERS 1996; 77:4664-4667. [PMID: 10062595 DOI: 10.1103/physrevlett.77.4664] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Nakanishi T, Ando T. Quantum interference effects in antidot lattices in magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8021-8027. [PMID: 9984479 DOI: 10.1103/physrevb.54.8021] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hackenbroich G, Weidenmüller HA. Conductance through a quantum dot in an Aharonov-Bohm ring. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:16379-16389. [PMID: 9983477 DOI: 10.1103/physrevb.53.16379] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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