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Geier M, Krøjer S, von Oppen F, Marcus CM, Flensberg K, Brouwer PW. Non-Abelian Holonomy of Majorana Zero Modes Coupled to a Chaotic Quantum Dot. PHYSICAL REVIEW LETTERS 2024; 132:036604. [PMID: 38307057 DOI: 10.1103/physrevlett.132.036604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Revised: 10/24/2023] [Accepted: 12/16/2023] [Indexed: 02/04/2024]
Abstract
If a quantum dot is coupled to a topological superconductor via tunneling contacts, each contact hosts a Majorana zero mode in the limit of zero transmission. Close to a resonance and at a finite contact transparency, the resonant level in the quantum dot couples the Majorana modes, but a ground-state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the dot is five or larger. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold is achieved. We characterize the corresponding non-Abelian holonomy for a quantum dot with chaotic classical dynamics using random matrix theory and discuss measurable signatures of the non-Abelian time evolution.
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Affiliation(s)
- Max Geier
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Svend Krøjer
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Physics Department, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Charles M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Karsten Flensberg
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Piet W Brouwer
- Dahlem Center for Complex Quantum Systems and Physics Department, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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Krich JJ, Halperin BI. Cubic Dresselhaus spin-orbit coupling in 2D electron quantum dots. PHYSICAL REVIEW LETTERS 2007; 98:226802. [PMID: 17677870 DOI: 10.1103/physrevlett.98.226802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2007] [Indexed: 05/16/2023]
Abstract
We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling (i.e., directly proportional p3) in GaAs/AlGaAs quantum dots. Using a semiclassical billiard model, we estimate the magnitude of the spin-orbit induced avoided crossings in a closed quantum dot in a Zeeman field. Using previous analyses based on random matrix theory, we calculate corresponding effects on the conductance through an open quantum dot. Combining our results with an experiment on an 8 microm2 quantum dot [D. M. Zumbühl, Phys. Rev. B 72, 081305 (2005)10.1103/PhysRevB.72.081305] suggests that (1) the GaAs Dresselhaus coupling constant gamma is approximately 9 eV A3, significantly less than the commonly cited value of 27.5 eV A3, and (2) the majority of the spin-flip effects can come from the cubic Dresselhaus term.
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Affiliation(s)
- Jacob J Krich
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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Debald S, Emary C. Spin-orbit-driven coherent oscillations in a few-electron quantum dot. PHYSICAL REVIEW LETTERS 2005; 94:226803. [PMID: 16090425 DOI: 10.1103/physrevlett.94.226803] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2004] [Indexed: 05/03/2023]
Abstract
We propose an experiment to observe coherent oscillations in a single quantum dot with the oscillations driven by spin-orbit interaction. This is achieved without spin-polarized leads, and relies on changing the strength of the spin-orbit coupling via an applied gate pulse. We derive an effective model of this system which is formally equivalent to the Jaynes-Cummings model of quantum optics. For parameters relevant to an InGaAs dot, we calculate a Rabi frequency of 2 GHz.
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Affiliation(s)
- Stefan Debald
- Institut für Theoretische Physik, Universität Hamburg, Jungiusstrasse 9, 20355 Hamburg, Germany
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Ghosh A, Ford CJB, Pepper M, Beere HE, Ritchie DA. Possible evidence of a spontaneous spin polarization in mesoscopic two-dimensional electron systems. PHYSICAL REVIEW LETTERS 2004; 92:116601. [PMID: 15089156 DOI: 10.1103/physrevlett.92.116601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2003] [Indexed: 05/24/2023]
Abstract
We have experimentally studied the nonequilibrium transport in low-density clean two-dimensional (2D) electron systems at mesoscopic length scales. At zero magnetic field (B), a double-peak structure in the nonlinear conductance was observed close to the Fermi energy in the localized regime. From the behavior of these peaks at nonzero B, we could associate them with the opposite spin states of the system, indicating a spontaneous spin polarization at B=0. Detailed temperature and disorder dependence of the structure shows that such a splitting is a ground-state property of low-density 2D systems.
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Affiliation(s)
- A Ghosh
- Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom
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Sharma P, Brouwer PW. Mesoscopic effects in adiabatic spin pumping. PHYSICAL REVIEW LETTERS 2003; 91:166801. [PMID: 14611425 DOI: 10.1103/physrevlett.91.166801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2003] [Indexed: 05/24/2023]
Abstract
We show that temporal shape modulations (pumping) of a quantum dot in the presence of spin-orbital coupling lead to a finite dc spin current. Depending on the strength of the spin-orbit coupling, the spin current is polarized perpendicular to the plane of the two-dimensional electron gas, or has an arbitrary direction subject to mesoscopic fluctuations. We analyze the statistics of the spin and charge currents in the adiabatic limit for the full crossover from weak to strong spin-orbit coupling.
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Affiliation(s)
- Prashant Sharma
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA
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Taylor JM, Marcus CM, Lukin MD. Long-lived memory for mesoscopic quantum bits. PHYSICAL REVIEW LETTERS 2003; 90:206803. [PMID: 12785914 DOI: 10.1103/physrevlett.90.206803] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2003] [Indexed: 05/24/2023]
Abstract
We describe a technique to create long-lived quantum memory for quantum bits in mesoscopic systems. Specifically we show that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei. The coherent transfer can be efficient and fast and it can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds. This method can also allow for "engineering" entangled states of nuclear ensembles and efficiently manipulating the stored states. We investigate the feasibility of this method through a detailed analysis of the coherence properties of the system.
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Affiliation(s)
- J M Taylor
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Held K, Eisenberg E, Altshuler BL. Random matrix theory for closed quantum dots with weak spin-orbit coupling. PHYSICAL REVIEW LETTERS 2003; 90:106802. [PMID: 12689023 DOI: 10.1103/physrevlett.90.106802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2002] [Indexed: 05/24/2023]
Abstract
To lowest order in the coupling strength, the spin-orbit coupling in quantum dots results in a spin-dependent Aharonov-Bohm flux. This flux decouples the spin-up and spin-down random matrix theory ensembles of the quantum dot. We employ this ensemble and find significant changes in the distribution of the Coulomb blockade peak height, in particular, a decrease of the width of the distribution. The puzzling disagreement between standard random matrix theory and the experimental distributions by Patel et al. [Phys. Rev. Lett. 81, 5900 (1998)]] might possibly be attributed to these spin-orbit effects.
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Affiliation(s)
- K Held
- Physics Department, Princeton University, Princeton, New Jersey 08544, USA.
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Zumbühl DM, Miller JB, Marcus CM, Campman K, Gossard AC. Spin-orbit coupling, antilocalization, and parallel magnetic fields in quantum dots. PHYSICAL REVIEW LETTERS 2002; 89:276803. [PMID: 12513231 DOI: 10.1103/physrevlett.89.276803] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2002] [Indexed: 05/24/2023]
Abstract
We investigate antilocalization due to spin-orbit coupling in ballistic GaAs quantum dots. Antilocalization that is prominent in large dots is suppressed in small dots, as anticipated theoretically. Parallel magnetic fields suppress both antilocalization and also, at larger fields, weak localization, consistent with random matrix theory results once orbital coupling of the parallel field is included. In situ control of spin-orbit coupling in dots is demonstrated as a gate-controlled crossover from weak localization to antilocalization.
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Affiliation(s)
- D M Zumbühl
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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Governale M. Quantum dots with Rashba spin-orbit coupling. PHYSICAL REVIEW LETTERS 2002; 89:206802. [PMID: 12443496 DOI: 10.1103/physrevlett.89.206802] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2002] [Indexed: 05/24/2023]
Abstract
We present results on the effects of spin-orbit coupling on the electronic structure of few-electron interacting quantum dots. The ground-state properties as a function of the number of electrons in the dot N are calculated by means of spin-density functional theory. We find a suppression of Hund's rule due to the competition of the Rashba effect and exchange interaction. Introducing an in-plane Zeeman field leads to a paramagnetic behavior of the dot in a closed-shell configuration and to spin texture in space.
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Affiliation(s)
- M Governale
- Institut für Theoretische Festkörperphysik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
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Mucciolo ER, Chamon C, Marcus CM. Adiabatic quantum pump of spin-polarized current. PHYSICAL REVIEW LETTERS 2002; 89:146802. [PMID: 12366064 DOI: 10.1103/physrevlett.89.146802] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2001] [Indexed: 05/23/2023]
Abstract
We propose a mechanism by which an open quantum dot driven by two ac (radio frequency) gate voltages in the presence of a moderate in-plane magnetic field generates a spin-polarized, phase-coherent dc current. The idea combines adiabatic, nonquantized (but coherent) pumping through periodically modulated external parameters and the strong fluctuations of the electron wave function existent in chaotic cavities. We estimate that the spin polarization of the current can be observed for temperatures and Zeeman splitting energies of the order of the single-particle mean level spacing.
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Affiliation(s)
- Eduardo R Mucciolo
- Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro, C.P. 38071, 22452-970 Rio de Janeiro, Brazil
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Aleiner IL, Fal'ko VI. Spin-orbit coupling effects on quantum transport in lateral semiconductor dots. PHYSICAL REVIEW LETTERS 2001; 87:256801. [PMID: 11736593 DOI: 10.1103/physrevlett.87.256801] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2001] [Indexed: 05/23/2023]
Abstract
The effects of interplay between spin-orbit coupling and Zeeman splitting on weak localization and universal conductance fluctuations in lateral semiconductor quantum dots are analyzed: All possible symmetry classes of corresponding random matrix theories are listed and crossovers between them achievable by sweeping magnetic field and changing the dot parameters are described. We also suggest experiments to measure the spin-orbit coupling constants.
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Affiliation(s)
- I L Aleiner
- Physics Department, Lancaster University, Lancaster L41 4YB, United Kingdom
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Folk JA, Patel SR, Birnbaum KM, Marcus CM, Duruöz CI, Harris JS. Spin degeneracy and conductance fluctuations in open quantum dots. PHYSICAL REVIEW LETTERS 2001; 86:2102-2105. [PMID: 11289865 DOI: 10.1103/physrevlett.86.2102] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2000] [Indexed: 05/23/2023]
Abstract
The dependence of conductance fluctuations on parallel magnetic field is used as a probe of spin degeneracy in open GaAs quantum dots. The variance of fluctuations at high parallel field is reduced from the low-field variance (with broken time-reversal symmetry) by factors ranging from roughly 2 in a 1 microm (2) dot to greater than 4 in 8 microm (2) dots. The factor of 2 is expected for Zeeman splitting of spin-degenerate channels. A possible explanation for the larger suppression based on field-dependent spin-orbit scattering is proposed.
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Affiliation(s)
- J A Folk
- Department of Physics, Stanford University, Stanford, California 94305, USA
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