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Yazdani A, von Oppen F, Halperin BI, Yacoby A. Hunting for Majoranas. Science 2023; 380:eade0850. [PMID: 37347870 DOI: 10.1126/science.ade0850] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 05/22/2023] [Indexed: 06/24/2023]
Abstract
Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.
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Affiliation(s)
- Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08540, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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2
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Feldman DE, Halperin BI. Fractional charge and fractional statistics in the quantum Hall effects. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:076501. [PMID: 34015771 DOI: 10.1088/1361-6633/ac03aa] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 05/20/2021] [Indexed: 06/12/2023]
Abstract
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.
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Affiliation(s)
- D E Feldman
- Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, RI 02912, United States of America
| | - Bertrand I Halperin
- Department of Physics, Harvard University, Cambridge, MA 02138, United States of America
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3
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Ma KKW, Wang R, Yang K. Realization of Supersymmetry and Its Spontaneous Breaking in Quantum Hall Edges. PHYSICAL REVIEW LETTERS 2021; 126:206801. [PMID: 34110185 DOI: 10.1103/physrevlett.126.206801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2021] [Accepted: 04/28/2021] [Indexed: 06/12/2023]
Abstract
Supersymmetry (SUSY) relating bosons and fermions plays an important role in unifying different fundamental interactions in particle physics. Since no superpartners of elementary particles have been observed, SUSY, if present, must be broken at low-energy. This makes it important to understand how SUSY is realized and broken, and study their consequences. We show that an N=(1,0) SUSY, arguably the simplest type, can be realized at the edge of the Moore-Read quantum Hall state. Depending on the absence or presence of edge reconstruction, both SUSY-preserving and SUSY broken phases can be realized in the same system, allowing for their unified description. The significance of the gapless fermionic Goldstino mode in the SUSY broken phase is discussed.
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Affiliation(s)
- Ken K W Ma
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Ruojun Wang
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Kun Yang
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
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4
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Kim Y, Herlinger P, Taniguchi T, Watanabe K, Smet JH. Reliable Postprocessing Improvement of van der Waals Heterostructures. ACS NANO 2019; 13:14182-14190. [PMID: 31775000 DOI: 10.1021/acsnano.9b06992] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The successful assembly of heterostructures consisting of several layers of different 2D materials in arbitrary order by exploiting van der Waals forces has truly been a game changer in the field of low-dimensional physics. For instance, the encapsulation of graphene or MoS2 between atomically flat hexagonal boron nitride (hBN) layers with strong affinity and graphitic gates that screen charge impurity disorder provided access to a plethora of interesting physical phenomena by drastically boosting the device quality. The encapsulation is accompanied by a self-cleansing effect at the interfaces. The otherwise predominant charged impurity disorder is minimized, and random strain fluctuations ultimately constitute the main source of residual disorder. Despite these advances, the fabricated heterostructures still vary notably in their performance. Although some achieve record mobilities, others only possess mediocre quality. Here, we report a reliable method to improve fully completed van der Waals heterostructure devices with a straightforward postprocessing surface treatment based on thermal annealing and contact mode atomic force microscopy (AFM). The impact is demonstrated by comparing magnetotransport measurements before and after the AFM treatment on one and the same device as well as on a larger set of treated and untreated devices to collect device statistics. Both the low-temperature properties and the room temperature electrical characteristics, as relevant for applications, improve on average substantially. We surmise that the main beneficial effect arises from reducing nanometer scale corrugations at the interfaces, that is, the detrimental impact of random strain fluctuations.
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Affiliation(s)
- Youngwook Kim
- Max-Planck-Institut für Festkörperforschung , 70569 Stuttgart , Germany
- Department of Emerging Materials Science , DGIST , 42988 Daegu , Korea
| | - Patrick Herlinger
- Max-Planck-Institut für Festkörperforschung , 70569 Stuttgart , Germany
| | - Takashi Taniguchi
- National Institute for Materials Science , 1-1 Namiki , Tsukuba 305-0044 , Japan
| | - Kenji Watanabe
- National Institute for Materials Science , 1-1 Namiki , Tsukuba 305-0044 , Japan
| | - Jurgen H Smet
- Max-Planck-Institut für Festkörperforschung , 70569 Stuttgart , Germany
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Falson J, Kawasaki M. A review of the quantum Hall effects in MgZnO/ZnO heterostructures. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:056501. [PMID: 29353814 DOI: 10.1088/1361-6633/aaa978] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This review visits recent experimental efforts on high mobility two-dimensional electron systems (2DES) hosted at the Mg x Zn[Formula: see text]O/ZnO heterointerface. We begin with the growth of these samples, and highlight the key characteristics of ozone-assisted molecular beam epitaxy required for their production. The transport characteristics of these structures are found to rival that of traditional semiconductor material systems, as signified by the high electron mobility ([Formula: see text] cm2 Vs-1) and rich quantum Hall features. Owing to a large effective mass and small dielectric constant, interaction effects are an order of magnitude stronger in comparison with the well studied GaAs-based 2DES. The strong correlation physics results in robust Fermi-liquid renormalization of the effective mass and spin susceptibility of carriers, which in turn dictates the parameter space for the quantum Hall effect. Finally, we explore the quantum Hall effect with a particular emphasis on the spin degree of freedom of carriers, and how their large spin splitting allows control of the ground states encountered at ultra-low temperatures within the fractional quantum Hall regime. We discuss in detail the physics of even-denominator fractional quantum Hall states, whose observation and underlying character remain elusive and exotic.
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Affiliation(s)
- Joseph Falson
- Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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6
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Li JIA, Tan C, Chen S, Zeng Y, Taniguchi T, Watanabe K, Hone J, Dean CR. Even-denominator fractional quantum Hall states in bilayer graphene. Science 2017; 358:648-652. [DOI: 10.1126/science.aao2521] [Citation(s) in RCA: 65] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Accepted: 09/25/2017] [Indexed: 12/13/2022]
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Jacak JE. Unconventional fractional quantum Hall effect in bilayer graphene. Sci Rep 2017; 7:8720. [PMID: 28821795 PMCID: PMC5562899 DOI: 10.1038/s41598-017-09166-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Accepted: 07/24/2017] [Indexed: 12/05/2022] Open
Abstract
Recent experimental progress in Hall measurements in bilayer graphene in the so-called open-face configuration of boron nitride encapsulated samples, together with the earlier technique of suspended samples, allows for precise observation of the fractional quantum Hall effect (FQHE) in all 4 subbands of the Lowest Landau level (with n = 0 and n = 1) and in the next LL subbands (with n = 2) in the bilayer system. Many newly observed FQHE features do not agree with a conventional model of composite fermions and reveal a different hierarchy in comparison to monolayer graphene or GaAs 2DEG. We explain the peculiarity of the FQHE hierarchy in the bilayer system in the framework of a topological approach, which includes the composite fermion model as its special case. Inclusion of a topological effect caused by the hopping of electrons between the two sheets in the bilayer system allowed for an explanation of the FQHE hierarchy in the graphene bilayer in satisfactory accordance with the experimental observations.
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Affiliation(s)
- Janusz Edward Jacak
- Department of Quantum Technologies, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspianskiego 27, 50-370, Wrocław, Poland.
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Leconte N, Kim H, Kim HJ, Ha DH, Watanabe K, Taniguchi T, Jung J, Jung S. Graphene bubbles and their role in graphene quantum transport. NANOSCALE 2017; 9:6041-6047. [PMID: 28443903 DOI: 10.1039/c7nr00339k] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Graphene bubbles are often formed when graphene and other layered two-dimensional materials are vertically stacked as van der Waals heterostructures. Here, we investigate how graphene bubbles and their related disorder impact the quantum transport behavior of graphene in the absence and presence of external magnetic fields. By combining experimental observations and numerical simulations, we find that the disorder induced by the graphene bubbles is mainly from p-type dopants and the charge transport in pristine graphene can be severely influenced by the presence of bubbles via long- and short-range scattering even with a small bubble-coverage of 2% and below. Upon bubble density increase, we observe an overall decrease in carrier mobility, and the appearance of a second Dirac point on the electron carrier side. At high magnetic fields, the disorder from graphene bubbles primarily impacts the quantization of the lowest Landau level, resulting in quantum Hall features associated with a new Dirac cone at high charge carrier density.
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Affiliation(s)
- Nicolas Leconte
- Department of Physics, University of Seoul, Seoul 02504, Korea.
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9
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Isobe H, Fu L. Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers. PHYSICAL REVIEW LETTERS 2017; 118:166401. [PMID: 28474921 DOI: 10.1103/physrevlett.118.166401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2016] [Indexed: 06/07/2023]
Abstract
We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum l=+1 are energetically favored for filling ν=1/2+1/2 and 1/4+1/4. The degeneracy between states with ±l is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.
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Affiliation(s)
- Hiroki Isobe
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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10
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Robust fractional quantum Hall effect in the N=2 Landau level in bilayer graphene. Nat Commun 2016; 7:13908. [PMID: 28000663 PMCID: PMC5187585 DOI: 10.1038/ncomms13908] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2016] [Accepted: 11/11/2016] [Indexed: 11/09/2022] Open
Abstract
The fractional quantum Hall effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most fractional quantum Hall studies have focussed on the lowest Landau level, whose fractional states are successfully explained by the composite fermion model. In the widely studied GaAs-based system, the composite fermion picture is thought to become unstable for the N≥2 Landau level, where competing many-body phases have been observed. Here we report magneto-resistance measurements of fractional quantum Hall states in the N=2 Landau level (filling factors 4<|ν|<8) in bilayer graphene. In contrast with recent observations of particle-hole asymmetry in the N=0/N=1 Landau levels of bilayer graphene, the fractional quantum Hall states we observe in the N=2 Landau level obey particle-hole symmetry within the fully symmetry-broken Landau level. Possible alternative ground states other than the composite fermions are discussed.
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11
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Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene. Sci Rep 2016; 6:38068. [PMID: 27905496 PMCID: PMC5131475 DOI: 10.1038/srep38068] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2016] [Accepted: 11/04/2016] [Indexed: 01/29/2023] Open
Abstract
Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.
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Zucker PT, Feldman DE. Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry. PHYSICAL REVIEW LETTERS 2016; 117:096802. [PMID: 27610872 DOI: 10.1103/physrevlett.117.096802] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Indexed: 06/06/2023]
Abstract
Numerical results suggest that the quantum Hall effect at ν=5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau-level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau-level mixing are strong. We show that the recent proposal of a particle-hole (PH)-Pfaffian topological order by Son is consistent with all experiments. The absence of particle-hole symmetry at ν=5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.
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Affiliation(s)
- P T Zucker
- Department of Physics, Brown University, Providence, Rhode Island 02912, USA
| | - D E Feldman
- Department of Physics, Brown University, Providence, Rhode Island 02912, USA
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Kim Y, Herlinger P, Moon P, Koshino M, Taniguchi T, Watanabe K, Smet JH. Charge Inversion and Topological Phase Transition at a Twist Angle Induced van Hove Singularity of Bilayer Graphene. NANO LETTERS 2016; 16:5053-5059. [PMID: 27387484 DOI: 10.1021/acs.nanolett.6b01906] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes, and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neighboring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a nonzero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.
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Affiliation(s)
- Youngwook Kim
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
| | - Patrick Herlinger
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
| | - Pilkyung Moon
- New York University , Shanghai 200120, China
- NYU-ECNU Institute of Physics at NYU Shanghai , Shanghai 200062, China
| | - Mikito Koshino
- Department of Physics, Tohoku University , Sendai 980-8578, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Kenji Watanabe
- National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Jurgen H Smet
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
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Shi Y, Lee Y, Che S, Pi Z, Espiritu T, Stepanov P, Smirnov D, Lau CN, Zhang F. Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2016; 116:056601. [PMID: 26894724 DOI: 10.1103/physrevlett.116.056601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Indexed: 06/05/2023]
Abstract
Owing to the spin, valley, and orbital symmetries, the lowest Landau level in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional quantum Hall (QH) states in bilayer graphene with controlled layer polarization. The state at filling factor ν=1 has two distinct phases: a layer polarized state that has a larger energy gap and is stabilized by high electric field, and a hitherto unobserved interlayer coherent state with a smaller gap that is stabilized by large magnetic field. In contrast, the ν=2/3 quantum Hall state and a feature at ν=1/2 are only resolved at finite electric field and large magnetic field. These results underscore the importance of controlling layer polarization in understanding the competing symmetries in the unusual QH system of BLG.
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Affiliation(s)
- Yanmeng Shi
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Yongjin Lee
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Shi Che
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Ziqi Pi
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Timothy Espiritu
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Petr Stepanov
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Dmitry Smirnov
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - Chun Ning Lau
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
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