1
|
Huang K, Fu H, Watanabe K, Taniguchi T, Zhu J. High-temperature quantum valley Hall effect with quantized resistance and a topological switch. Science 2024; 385:657-661. [PMID: 39024378 DOI: 10.1126/science.adj3742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 07/08/2024] [Indexed: 07/20/2024]
Abstract
Edge states of a topological insulator can be used to explore fundamental science emerging at the interface of low dimensionality and topology. Achieving a robust conductance quantization, however, has proven challenging for helical edge states. In this work, we show wide resistance plateaus in kink states-a manifestation of the quantum valley Hall effect in Bernal bilayer graphene-quantized to the predicted value at zero magnetic field. The plateau resistance has a very weak temperature dependence up to 50 kelvin and is flat within a dc bias window of tens of millivolts. We demonstrate the electrical operation of a topology-controlled switch with an on/off ratio of 200. These results demonstrate the robustness and tunability of the kink states and its promise in constructing electron quantum optics devices.
Collapse
Affiliation(s)
- Ke Huang
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
- Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, PA 16802, USA
| |
Collapse
|
2
|
Interplay between topological valley and quantum Hall edge transport. Nat Commun 2022; 13:4187. [PMID: 35858959 PMCID: PMC9300606 DOI: 10.1038/s41467-022-31680-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 06/21/2022] [Indexed: 11/08/2022] Open
Abstract
An established way of realising topologically protected states in a two-dimensional electron gas is by applying a perpendicular magnetic field thus creating quantum Hall edge channels. In electrostatically gapped bilayer graphene intriguingly, even in the absence of a magnetic field, topologically protected electronic states can emerge at naturally occurring stacking domain walls. While individually both types of topologically protected states have been investigated, their intriguing interplay remains poorly understood. Here, we focus on the interplay between topological domain wall states and quantum Hall edge transport within the eight-fold degenerate zeroth Landau level of high-quality suspended bilayer graphene. We find that the two-terminal conductance remains approximately constant for low magnetic fields throughout the distinct quantum Hall states since the conduction channels are traded between domain wall and device edges. For high magnetic fields, however, we observe evidence of transport suppression at the domain wall, which can be attributed to the emergence of spectral minigaps. This indicates that stacking domain walls potentially do not correspond to a topological domain wall in the order parameter.
Collapse
|
3
|
Wieder BJ, Bradlyn B, Wang Z, Cano J, Kim Y, Kim HSD, Rappe AM, Kane CL, Bernevig BA. Wallpaper fermions and the nonsymmorphic Dirac insulator. Science 2018; 361:246-251. [DOI: 10.1126/science.aan2802] [Citation(s) in RCA: 100] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Accepted: 05/22/2018] [Indexed: 01/25/2023]
Affiliation(s)
- Benjamin J. Wieder
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
- Nordita, Center for Quantum Materials, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6323, USA
| | - Barry Bradlyn
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA
| | - Zhijun Wang
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Jennifer Cano
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA
| | - Youngkuk Kim
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323, USA
- Department of Physics, Sungkyunkwan University (SKKU), Suwon 16419, Korea
| | - Hyeong-Seok D. Kim
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6323, USA
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323, USA
| | - Andrew M. Rappe
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323, USA
| | - C. L. Kane
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6323, USA
| | - B. Andrei Bernevig
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
- Max Planck Institute of Microstructure Physics, 06120 Halle, Germany
| |
Collapse
|
4
|
Realisation of topological zero-energy mode in bilayer graphene in zero magnetic field. Sci Rep 2017; 7:6466. [PMID: 28743948 PMCID: PMC5527089 DOI: 10.1038/s41598-017-06902-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2017] [Accepted: 06/20/2017] [Indexed: 12/03/2022] Open
Abstract
Bilayer graphene (BLG) gapped by a vertical electric field represents a valley-symmetry-protected topological insulating state. Emergence of a new topological zero-energy mode has been proposed in BLG at a boundary between regions of inverted band gaps induced by two oppositely polarized vertical electric fields. However, its realisation has been challenged by the enormous difficulty in arranging two pairs of accurately aligned split gates on the top and bottom surfaces of clean BLG. Here we report realisation of the topological zero-energy mode in ballistic BLG, with zero-bias differential conductance close to the ideal value of 4 e2/h (e is the electron charge and h is Planck’s constant) along a boundary channel between a pair of gate-defined inverted band gaps. This constitutes the bona fide electrical-gate-tuned generation of a valley-symmetry-protected topological boundary conducting channel in BLG in zero magnetic field, which is essential to valleytronics applications of BLG.
Collapse
|
5
|
Ren Y, Qiao Z, Niu Q. Topological phases in two-dimensional materials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:066501. [PMID: 27176924 DOI: 10.1088/0034-4885/79/6/066501] [Citation(s) in RCA: 104] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as [Formula: see text] topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.
Collapse
Affiliation(s)
- Yafei Ren
- ICQD, Hefei National Laboratory for Physical Sciences at Microscale, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China. CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | | | | |
Collapse
|
6
|
Li X, Zhang F, Niu Q, MacDonald AH. Spontaneous layer-pseudospin domain walls in bilayer graphene. PHYSICAL REVIEW LETTERS 2014; 113:116803. [PMID: 25259998 DOI: 10.1103/physrevlett.113.116803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2014] [Indexed: 06/03/2023]
Abstract
Bilayer graphene is susceptible to a family of unusual broken symmetry states with spin and valley dependent layer polarization. We report on a microscopic study of the domain walls in these systems, demonstrating that they have interesting microscopic structure related to the topological character of the ordered states. We use our results to show that the metal-insulator transition temperature in bilayer graphene is reduced from mean-field estimates by thermal excitation of domain walls.
Collapse
Affiliation(s)
- Xiao Li
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Qian Niu
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA and School of Physics, International Center for Quantum Materials and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
| | - A H MacDonald
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| |
Collapse
|
7
|
McCann E, Koshino M. The electronic properties of bilayer graphene. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:056503. [PMID: 23604050 DOI: 10.1088/0034-4885/76/5/056503] [Citation(s) in RCA: 208] [Impact Index Per Article: 18.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.
Collapse
Affiliation(s)
- Edward McCann
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
| | | |
Collapse
|
8
|
Jung J, Qiao Z, Niu Q, Macdonald AH. Transport properties of graphene nanoroads in boron nitride sheets. NANO LETTERS 2012; 12:2936-2940. [PMID: 22524401 DOI: 10.1021/nl300610w] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We demonstrate that the one-dimensional (1D) transport channels that appear in the gap when graphene nanoroads are embedded in boron nitride (BN) sheets are more robust when they are inserted at AB/BA grain boundaries. Our conclusions are based on ab initio electronic structure calculations for a variety of different crystal orientations and bonding arrangements at the BN/C interfaces. This property is related to the valley Hall conductivity present in the BN band structure and to the topologically protected kink states that appear in continuum Dirac models with position-dependent masses.
Collapse
Affiliation(s)
- Jeil Jung
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States
| | | | | | | |
Collapse
|
9
|
Killi M, Wu S, Paramekanti A. Band structures of bilayer graphene superlattices. PHYSICAL REVIEW LETTERS 2011; 107:086801. [PMID: 21929188 DOI: 10.1103/physrevlett.107.086801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2011] [Indexed: 05/31/2023]
Abstract
We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero-energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of "topological" edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.
Collapse
Affiliation(s)
- Matthew Killi
- Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
| | | | | |
Collapse
|
10
|
Qiao Z, Jung J, Niu Q, Macdonald AH. Electronic highways in bilayer graphene. NANO LETTERS 2011; 11:3453-3459. [PMID: 21766817 DOI: 10.1021/nl201941f] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Bilayer graphene with an interlayer potential difference has an energy gap and, when the potential difference varies spatially, topologically protected one-dimensional states localized along the difference's zero lines. When disorder is absent, electronic travel directions along zero-line trajectories are fixed by valley Hall properties. Using the Landauer-Büttiker formula and the nonequilibrium Green's function technique, we demonstrate numerically that collisions between electrons traveling in opposite directions, due to either disorder or changes in path direction, are strongly suppressed. We find that extremely long mean free paths of the order of hundreds of micrometers can be expected in relatively clean samples. This finding suggests the possibility of designing low power nanoscale electronic devices in which transport paths are controlled by gates which alter the interlayer potential landscape.
Collapse
Affiliation(s)
- Zhenhua Qiao
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States.
| | | | | | | |
Collapse
|
11
|
Zarenia M, Pereira JM, Peeters FM, de Aquino Farias G. Topological confinement in an antisymmetric potential in bilayer graphene in the presence of a magnetic field. NANOSCALE RESEARCH LETTERS 2011; 6:452. [PMID: 21756331 PMCID: PMC3211872 DOI: 10.1186/1556-276x-6-452] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2010] [Accepted: 07/14/2011] [Indexed: 05/12/2023]
Abstract
We investigate the effect of an external magnetic field on the carrier states that are localized at a potential kink and a kink-antikink in bilayer graphene. These chiral states are localized at the interface between two potential regions with opposite signs.PACS numbers: 71.10.Pm, 73.21.-b, 81.05.Uw.
Collapse
Affiliation(s)
- Mohammad Zarenia
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
| | - Joao Milton Pereira
- Departamento de Física, Universidade Federal do Ceará, Fortaleza, Ceará, 60455-760, Brazil
| | - François Maria Peeters
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
- Departamento de Física, Universidade Federal do Ceará, Fortaleza, Ceará, 60455-760, Brazil
| | - Gil de Aquino Farias
- Departamento de Física, Universidade Federal do Ceará, Fortaleza, Ceará, 60455-760, Brazil
| |
Collapse
|