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Hecker K, Banszerus L, Schäpers A, Möller S, Peters A, Icking E, Watanabe K, Taniguchi T, Volk C, Stampfer C. Coherent charge oscillations in a bilayer graphene double quantum dot. Nat Commun 2023; 14:7911. [PMID: 38036517 PMCID: PMC10689829 DOI: 10.1038/s41467-023-43541-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 11/13/2023] [Indexed: 12/02/2023] Open
Abstract
The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-Stückelberg-Majorana (LZSM) interference. LZSM interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and [Formula: see text] charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZSM interference and photon assisted tunneling. Both techniques yield [Formula: see text] average values in the range of 400-500 ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments.
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Affiliation(s)
- K Hecker
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074, Aachen, Germany.
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425, Jülich, Germany.
| | - L Banszerus
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425, Jülich, Germany
| | - A Schäpers
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074, Aachen, Germany
| | - S Möller
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425, Jülich, Germany
| | - A Peters
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074, Aachen, Germany
| | - E Icking
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425, Jülich, Germany
| | - K Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - T Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - C Volk
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425, Jülich, Germany
| | - C Stampfer
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425, Jülich, Germany
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Banszerus L, Möller S, Hecker K, Icking E, Watanabe K, Taniguchi T, Hassler F, Volk C, Stampfer C. Particle-hole symmetry protects spin-valley blockade in graphene quantum dots. Nature 2023:10.1038/s41586-023-05953-5. [PMID: 37138084 DOI: 10.1038/s41586-023-05953-5] [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] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 03/14/2023] [Indexed: 05/05/2023]
Abstract
Particle-hole symmetry plays an important role in the characterization of topological phases in solid-state systems1. It is found, for example, in free-fermion systems at half filling and it is closely related to the notion of antiparticles in relativistic field theories2. In the low-energy limit, graphene is a prime example of a gapless particle-hole symmetric system described by an effective Dirac equation3,4 in which topological phases can be understood by studying ways to open a gap by preserving (or breaking) symmetries5,6. An important example is the intrinsic Kane-Mele spin-orbit gap of graphene, which leads to a lifting of the spin-valley degeneracy and renders graphene a topological insulator in a quantum spin Hall phase7 while preserving particle-hole symmetry. Here we show that bilayer graphene allows the realization of electron-hole double quantum dots that exhibit near-perfect particle-hole symmetry, in which transport occurs via the creation and annihilation of single electron-hole pairs with opposite quantum numbers. Moreover, we show that particle-hole symmetric spin and valley textures lead to a protected single-particle spin-valley blockade. The latter will allow robust spin-to-charge and valley-to-charge conversion, which are essential for the operation of spin and valley qubits.
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Affiliation(s)
- L Banszerus
- JARA-FIT and 2nd Institute of Physics A, RWTH Aachen University, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - S Möller
- JARA-FIT and 2nd Institute of Physics A, RWTH Aachen University, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - K Hecker
- JARA-FIT and 2nd Institute of Physics A, RWTH Aachen University, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - E Icking
- JARA-FIT and 2nd Institute of Physics A, RWTH Aachen University, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - K Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - T Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - F Hassler
- JARA-Institute for Quantum Information, RWTH Aachen University, Aachen, Germany
| | - C Volk
- JARA-FIT and 2nd Institute of Physics A, RWTH Aachen University, Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - C Stampfer
- JARA-FIT and 2nd Institute of Physics A, RWTH Aachen University, Aachen, Germany.
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany.
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Möller S, Banszerus L, Knothe A, Steiner C, Icking E, Trellenkamp S, Lentz F, Watanabe K, Taniguchi T, Glazman LI, Fal'ko VI, Volk C, Stampfer C. Probing Two-Electron Multiplets in Bilayer Graphene Quantum Dots. Phys Rev Lett 2021; 127:256802. [PMID: 35029428 DOI: 10.1103/physrevlett.127.256802] [Citation(s) in RCA: 2] [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: 06/16/2021] [Accepted: 11/01/2021] [Indexed: 05/21/2023]
Abstract
We report on finite bias spectroscopy measurements of the two-electron spectrum in a gate defined bilayer graphene (BLG) quantum dot for varying magnetic fields. The spin and valley degree of freedom in BLG give rise to multiplets of six orbital symmetric and ten orbital antisymmetric states. We find that orbital symmetric states are lower in energy and separated by ≈ 0.4-0.8 meV from orbital antisymmetric states. The symmetric multiplet exhibits an additional energy splitting of its six states of ≈ 0.15-0.5 meV due to lattice scale interactions. The experimental observations are supported by theoretical calculations, which allow to determine that intervalley scattering and "current-current" interaction constants are of the same magnitude in BLG.
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Affiliation(s)
- S Möller
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich 52425, Germany
| | - L Banszerus
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich 52425, Germany
| | - A Knothe
- National Graphene Institute, University of Manchester, Manchester M13 9PL, United Kingdom
| | - C Steiner
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany
| | - E Icking
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich 52425, Germany
| | - S Trellenkamp
- Helmholtz Nano Facility, Forschungszentrum Jülich, Jülich 52425, Germany
| | - F Lentz
- Helmholtz Nano Facility, Forschungszentrum Jülich, Jülich 52425, Germany
| | - K Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - T Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - L I Glazman
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - V I Fal'ko
- National Graphene Institute, University of Manchester, Manchester M13 9PL, United Kingdom
- Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
- Henry Royce Institute for Advanced Materials, University of Manchester, Manchester M13 9PL, United Kingdom
| | - C Volk
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich 52425, Germany
| | - C Stampfer
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich 52425, Germany
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Banszerus L, Möller S, Steiner C, Icking E, Trellenkamp S, Lentz F, Watanabe K, Taniguchi T, Volk C, Stampfer C. Spin-valley coupling in single-electron bilayer graphene quantum dots. Nat Commun 2021; 12:5250. [PMID: 34475394 PMCID: PMC8413270 DOI: 10.1038/s41467-021-25498-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [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: 03/17/2021] [Accepted: 08/13/2021] [Indexed: 11/30/2022] Open
Abstract
Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μeV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the \documentclass[12pt]{minimal}
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\begin{document}$$K^{\prime}$$\end{document}K′ states below 20 μeV. Understanding the interaction between spin and valley degrees of freedom in graphene-based quantum dots underpins their applications in electronics and quantum information. Here, the authors study the low-energy spectrum and resolve the spin-valley coupling in single-electron quantum dots in bilayer graphene.
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Affiliation(s)
- L Banszerus
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen, Germany. .,Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany.
| | - S Möller
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen, Germany.,Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - C Steiner
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen, Germany.,Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - E Icking
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen, Germany.,Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - S Trellenkamp
- Helmholtz Nano Facility, Forschungszentrum Jülich, Jülich, Germany
| | - F Lentz
- Helmholtz Nano Facility, Forschungszentrum Jülich, Jülich, Germany
| | - K Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - T Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - C Volk
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen, Germany.,Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
| | - C Stampfer
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen, Germany.,Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany
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5
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Banszerus L, Rothstein A, Fabian T, Möller S, Icking E, Trellenkamp S, Lentz F, Neumaier D, Watanabe K, Taniguchi T, Libisch F, Volk C, Stampfer C. Electron-Hole Crossover in Gate-Controlled Bilayer Graphene Quantum Dots. Nano Lett 2020; 20:7709-7715. [PMID: 32986437 PMCID: PMC7564435 DOI: 10.1021/acs.nanolett.0c03227] [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] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Revised: 09/28/2020] [Indexed: 05/21/2023]
Abstract
Electron and hole Bloch states in bilayer graphene exhibit topological orbital magnetic moments with opposite signs, which allows for tunable valley-polarization in an out-of-plane magnetic field. This property makes electron and hole quantum dots (QDs) in bilayer graphene interesting for valley and spin-valley qubits. Here, we show measurements of the electron-hole crossover in a bilayer graphene QD, demonstrating opposite signs of the magnetic moments associated with the Berry curvature. Using three layers of top gates, we independently control the tunneling barriers while tuning the occupation from the few-hole regime to the few-electron regime, crossing the displacement-field-controlled band gap. The band gap is around 25 meV, while the charging energies of the electron and hole dots are between 3 and 5 meV. The extracted valley g-factor is around 17 and leads to opposite valley polarization for electrons and holes at moderate B-fields. Our measurements agree well with tight-binding calculations for our device.
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Affiliation(s)
- L. Banszerus
- JARA-FIT
and 2nd Institute of Physics, RWTH Aachen
University, 52074 Aachen, Germany, E.U
- Peter
Grünberg Institute (PGI-9), Forschungszentrum
Jülich, 52425 Jülich, Germany, E.U
| | - A. Rothstein
- JARA-FIT
and 2nd Institute of Physics, RWTH Aachen
University, 52074 Aachen, Germany, E.U
| | - T. Fabian
- Institute
for Theoretical Physics, TU Wien, 1040 Vienna, Austria, E.U
| | - S. Möller
- JARA-FIT
and 2nd Institute of Physics, RWTH Aachen
University, 52074 Aachen, Germany, E.U
- Peter
Grünberg Institute (PGI-9), Forschungszentrum
Jülich, 52425 Jülich, Germany, E.U
| | - E. Icking
- JARA-FIT
and 2nd Institute of Physics, RWTH Aachen
University, 52074 Aachen, Germany, E.U
- Peter
Grünberg Institute (PGI-9), Forschungszentrum
Jülich, 52425 Jülich, Germany, E.U
| | - S. Trellenkamp
- Helmholtz
Nano Facility, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - F. Lentz
- Helmholtz
Nano Facility, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - D. Neumaier
- AMO
GmbH, Gesellschaft für
Angewandte Mikro- und Optoelektronik, 52074 Aachen, Germany, E.U
- University
of Wuppertal, 42285 Wuppertal, Germany, E.U
| | - K. Watanabe
- Research
Center for Functional Materials, National
Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - T. Taniguchi
- International
Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - F. Libisch
- Institute
for Theoretical Physics, TU Wien, 1040 Vienna, Austria, E.U
| | - C. Volk
- JARA-FIT
and 2nd Institute of Physics, RWTH Aachen
University, 52074 Aachen, Germany, E.U
- Peter
Grünberg Institute (PGI-9), Forschungszentrum
Jülich, 52425 Jülich, Germany, E.U
| | - C. Stampfer
- JARA-FIT
and 2nd Institute of Physics, RWTH Aachen
University, 52074 Aachen, Germany, E.U
- Peter
Grünberg Institute (PGI-9), Forschungszentrum
Jülich, 52425 Jülich, Germany, E.U
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