1
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Han T, Lu Z, Scuri G, Sung J, Wang J, Han T, Watanabe K, Taniguchi T, Park H, Ju L. Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene. NATURE NANOTECHNOLOGY 2024; 19:181-187. [PMID: 37798567 DOI: 10.1038/s41565-023-01520-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 09/04/2023] [Indexed: 10/07/2023]
Abstract
Rhombohedral-stacked multilayer graphene hosts a pair of flat bands touching at zero energy, which should give rise to correlated electron phenomena that can be tuned further by an electric field. Moreover, when electron correlation breaks the isospin symmetry, the valley-dependent Berry phase at zero energy may give rise to topologically non-trivial states. Here we measure electron transport through hexagonal boron nitride-encapsulated pentalayer graphene down to 100 mK. We observed a correlated insulating state with resistance at the megaohm level or greater at charge density n = 0 and displacement field D = 0. Tight-binding calculations predict a metallic ground state under these conditions. By increasing D, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a magnetic field of around 1 T. At high D and n, we observed isospin-polarized quarter- and half-metals. Hence, rhombohedral pentalayer graphene exhibits two different types of Fermi-surface instability, one driven by a pair of flat bands touching at zero energy, and one induced by the Stoner mechanism in a single flat band. Our results establish rhombohedral multilayer graphene as a suitable system for exploring intertwined electron correlation and topology phenomena in natural graphitic materials without the need for moiré superlattice engineering.
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Affiliation(s)
- Tonghang Han
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Zhengguang Lu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Giovanni Scuri
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Jiho Sung
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Jue Wang
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Tianyi Han
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Hongkun Park
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Long Ju
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
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Geisenhof FR, Winterer F, Seiler AM, Lenz J, Zhang F, Weitz RT. Impact of Electric Field Disorder on Broken-Symmetry States in Ultraclean Bilayer Graphene. NANO LETTERS 2022; 22:7378-7385. [PMID: 36113049 DOI: 10.1021/acs.nanolett.2c02119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Bilayer graphene (BLG) has multiple internal degrees of freedom and a constant density of states down to the charge neutrality point when trigonal warping is ignored. Consequently, it is susceptible to various competing ground states. However, a coherent experimental determination of the ground state has been challenging due to the interaction-disorder interplay. Here we present an extensive transport study in a series of dually gated freestanding BLG devices and identify the layer-antiferromagnet as the ground state with a continuous strength across all devices. This strength correlates with the width of the state in the electric field. We systematically identify electric-field disorder─spatial variations in the interlayer potential difference─as the main source responsible for the observations. Our results pinpoint for the first time the importance of electric-field disorder on spontaneous symmetry breaking in BLG and solve a long-standing debate on its ground state. The electric-field disorder should be universal to all 2D materials.
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Affiliation(s)
- Fabian R Geisenhof
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, Munich 80539, Germany
| | - Felix Winterer
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, Munich 80539, Germany
| | - Anna M Seiler
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, Munich 80539, Germany
- 1st Physical Institute, Faculty of Physics, University of Göttingen, Friedrich-Hund-Platz 1, Göttingen 37077, Germany
| | - Jakob Lenz
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, Munich 80539, Germany
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, United States
| | - R Thomas Weitz
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, Munich 80539, Germany
- Center for Nanoscience (CeNS), Schellingstrasse 4, Munich 80799, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, Munich 80799, Germany
- 1st Physical Institute, Faculty of Physics, University of Göttingen, Friedrich-Hund-Platz 1, Göttingen 37077, Germany
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3
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Quantum cascade of correlated phases in trigonally warped bilayer graphene. Nature 2022; 608:298-302. [PMID: 35948716 DOI: 10.1038/s41586-022-04937-1] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2021] [Accepted: 06/07/2022] [Indexed: 11/08/2022]
Abstract
Divergent density of states offers an opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultraflat bands of magic-angle twisted bilayer graphene1-5, the band touching points of few-layer rhombohedral graphite6-8 and the lightly doped rhombohedral trilayer graphene9-11. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism at charge neutrality7 leading to layer antiferromagnetic states12 or quantum anomalous Hall states13. Here we report the observation of a cascade of correlated phases in the vicinity of electric-field-controlled Lifshitz transitions14,15 and van Hove singularities16 in Bernal bilayer graphene. We provide evidence for the observation of Stoner ferromagnets in the form of half and quarter metals10,11. Furthermore, we identify signatures consistent with a topologically non-trivial Wigner-Hall crystal17 at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behaviour deviates from that of standard Fermi liquids. Our results in this reproducible, tunable, simple system open up new horizons for studying strongly correlated electrons.
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4
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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.
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5
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Zhou H, Holleis L, Saito Y, Cohen L, Huynh W, Patterson CL, Yang F, Taniguchi T, Watanabe K, Young AF. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 2022; 375:774-778. [PMID: 35025604 DOI: 10.1126/science.abm8386] [Citation(s) in RCA: 41] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by a large applied perpendicular electric field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite magnetic field B‖ ≈ 150 milliteslas applied parallel to the two-dimensional sheet. Superconductivity occurs near a symmetry-breaking transition and exists exclusively above the B‖ limit expected of a paramagnetic superconductor with the observed transition critical temperature TC ≈ 30 millikelvins, consistent with a spin-triplet order parameter.
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Affiliation(s)
- Haoxin Zhou
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Ludwig Holleis
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Yu Saito
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Liam Cohen
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - William Huynh
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Caitlin L Patterson
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Fangyuan Yang
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Andrea F Young
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
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6
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Geisenhof FR, Winterer F, Seiler AM, Lenz J, Xu T, Zhang F, Weitz RT. Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene. Nature 2021; 598:53-58. [PMID: 34616059 DOI: 10.1038/s41586-021-03849-w] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Accepted: 07/22/2021] [Indexed: 11/09/2022]
Abstract
The quantum anomalous Hall (QAH) effect-a macroscopic manifestation of chiral band topology at zero magnetic field-has been experimentally realized only by the magnetic doping of topological insulators1-3 and the delicate design of moiré heterostructures4-8. However, the seemingly simple bilayer graphene without magnetic doping or moiré engineering has long been predicted to host competing ordered states with QAH effects9-11. Here we explore states in bilayer graphene with a conductance of 2 e2 h-1 (where e is the electronic charge and h is Planck's constant) that not only survive down to anomalously small magnetic fields and up to temperatures of five kelvin but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital-magnetism-driven QAH behaviour that is tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations owing to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley and spin-valley Hall behaviour9.
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Affiliation(s)
- Fabian R Geisenhof
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Felix Winterer
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Anna M Seiler
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Jakob Lenz
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Tianyi Xu
- Department of Physics, University of Texas at Dallas, Richardson, TX, USA
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, TX, USA.
| | - R Thomas Weitz
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany. .,Center for Nanoscience (CeNS), Munich, Germany. .,Munich Center for Quantum Science and Technology (MCQST), Munich, Germany. .,1st Physical Institute, Faculty of Physics, University of Göttingen, Göttingen, Germany.
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7
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Tanaka M, Shimazaki Y, Borzenets IV, Watanabe K, Taniguchi T, Tarucha S, Yamamoto M. Charge Neutral Current Generation in a Spontaneous Quantum Hall Antiferromagnet. PHYSICAL REVIEW LETTERS 2021; 126:016801. [PMID: 33480769 DOI: 10.1103/physrevlett.126.016801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 10/12/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
The intrinsic Hall effect allows for the generation of a nondissipative charge neutral current, such as a pure spin current generated via the spin Hall effect. Breaking of the spatial inversion or time reversal symmetries, or the spin-orbit interaction is generally considered necessary for the generation of such a charge neutral current. Here, we challenge this general concept and present generation and detection of a charge neutral current in a centrosymmetric material with little spin-orbit interaction. We employ bilayer graphene, and find enhanced nonlocal transport in the quantum Hall antiferromagnetic state, where spontaneous symmetry breaking occurs due to the electronic correlation.
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Affiliation(s)
- Miuko Tanaka
- Department of Applied Physics, University of Tokyo, Tokyo, 113-8656, Japan
| | - Yuya Shimazaki
- Institute of Quantum Electronics, ETH Zurich, CH-8093, Zurich, Switzerland
| | | | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, 305-0044, Japan
| | - Seigo Tarucha
- Center for Emergent Matter Science, RIKEN, Wako, 351-0198, Japan
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8
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Zheng Z, Ma Q, Bi Z, de la Barrera S, Liu MH, Mao N, Zhang Y, Kiper N, Watanabe K, Taniguchi T, Kong J, Tisdale WA, Ashoori R, Gedik N, Fu L, Xu SY, Jarillo-Herrero P. Unconventional ferroelectricity in moiré heterostructures. Nature 2020; 588:71-76. [DOI: 10.1038/s41586-020-2970-9] [Citation(s) in RCA: 77] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2020] [Accepted: 10/07/2020] [Indexed: 11/09/2022]
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9
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Wagner G, Nguyen DX, Simon SH. Transport in Bilayer Graphene near Charge Neutrality: Which Scattering Mechanisms Are Important? PHYSICAL REVIEW LETTERS 2020; 124:026601. [PMID: 32004029 DOI: 10.1103/physrevlett.124.026601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Indexed: 06/10/2023]
Abstract
Using the semiclassical quantum Boltzmann equation (QBE), we numerically calculate the dc transport properties of bilayer graphene near charge neutrality. We find, in contrast to prior discussions, that phonon scattering is crucial even at temperatures below 40 K. Nonetheless, electron-electron scattering still dominates over phonon collisions allowing a hydrodynamic approach. We introduce a simple two-fluid hydrodynamic model of electrons and holes interacting via Coulomb drag and compare our results to the full QBE calculation. We show that the two-fluid model produces quantitatively accurate results for conductivity, thermopower, and thermal conductivity.
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Affiliation(s)
- Glenn Wagner
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Dung X Nguyen
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Steven H Simon
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
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10
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Li J, Fu H, Yin Z, Watanabe K, Taniguchi T, Zhu J. Metallic Phase and Temperature Dependence of the ν=0 Quantum Hall State in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2019; 122:097701. [PMID: 30932549 DOI: 10.1103/physrevlett.122.097701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Indexed: 06/09/2023]
Abstract
The ν=0 quantum Hall state of bilayer graphene is a fertile playground to realize many-body ground states with various broken symmetries. Here we report the experimental observations of a previously unreported metallic phase. The metallic phase resides in the phase space between the previously identified layer polarized state at large transverse electric field and the canted antiferromagnetic state at small transverse electric field. We also report temperature dependence studies of the quantum spin Hall state of ν=0. Complex nonmonotonic behavior reveals concomitant bulk and edge conductions and excitations. These results provide a timely experimental update to understand the rich physics of the ν=0 state.
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Affiliation(s)
- Jing Li
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Zhenxi Yin
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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11
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Nam Y, Ki DK, Soler-Delgado D, Morpurgo AF. A family of finite-temperature electronic phase transitions in graphene multilayers. Science 2018; 362:324-328. [PMID: 30337406 DOI: 10.1126/science.aar6855] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Accepted: 08/28/2018] [Indexed: 12/24/2022]
Abstract
Suspended Bernal-stacked graphene multilayers up to an unexpectedly large thickness exhibit a broken-symmetry ground state whose origin remains to be understood. We show that a finite-temperature second-order phase transition occurs in multilayers whose critical temperature (T c) increases from 12 kelvins (K) in bilayers to 100 K in heptalayers. A comparison of the data with a phenomenological model inspired by a mean-field approach suggests that the transition is associated with the appearance of a self-consistent valley- and spin-dependent staggered potential that changes sign from one layer to the next, appearing at T c and increasing upon cooling. The systematic evolution with thickness of several measured quantities imposes constraints on any microscopic theory aiming to analyze the nature of electronic correlations in this system.
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Affiliation(s)
- Youngwoo Nam
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.,Department of Physics, Gyeongsang National University, Jinju-daero 501, Jinju-si, South Korea
| | - Dong-Keun Ki
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.,Department of Physics, The University of Hong Kong, Hong Kong, China
| | - David Soler-Delgado
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland
| | - Alberto F Morpurgo
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.
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12
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Shi Y, Che S, Zhou K, Ge S, Pi Z, Espiritu T, Taniguchi T, Watanabe K, Barlas Y, Lake R, Lau CN. Tunable Lifshitz Transitions and Multiband Transport in Tetralayer Graphene. PHYSICAL REVIEW LETTERS 2018; 120:096802. [PMID: 29547315 DOI: 10.1103/physrevlett.120.096802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Indexed: 06/08/2023]
Abstract
As the Fermi level and band structure of two-dimensional materials are readily tunable, they constitute an ideal platform for exploring the Lifshitz transition, a change in the topology of a material's Fermi surface. Using tetralayer graphene that host two intersecting massive Dirac bands, we demonstrate multiple Lifshitz transitions and multiband transport, which manifest as a nonmonotonic dependence of conductivity on the charge density n and out-of-plane electric field D, anomalous quantum Hall sequences and Landau level crossings that evolve with n, D, and B.
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Affiliation(s)
- Yanmeng Shi
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Shi Che
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Kuan Zhou
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Supeng Ge
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Ziqi Pi
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Timothy Espiritu
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Yafis Barlas
- Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, California 92521, USA
| | - Roger Lake
- Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, California 92521, USA
| | - Chun Ning Lau
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, USA
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
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13
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Shallcross S, Sharma S, Weber HB. Anomalous Dirac point transport due to extended defects in bilayer graphene. Nat Commun 2017; 8:342. [PMID: 28839136 PMCID: PMC5571127 DOI: 10.1038/s41467-017-00397-8] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2016] [Accepted: 06/27/2017] [Indexed: 11/21/2022] Open
Abstract
Charge transport at the Dirac point in bilayer graphene exhibits two dramatically different transport states, insulating and metallic, that occur in apparently otherwise indistinguishable experimental samples. We demonstrate that the existence of these two transport states has its origin in an interplay between evanescent modes, that dominate charge transport near the Dirac point, and disordered configurations of extended defects in the form of partial dislocations. In a large ensemble of bilayer systems with randomly positioned partial dislocations, the distribution of conductivities is found to be strongly peaked at both the insulating and metallic limits. We argue that this distribution form, that occurs only at the Dirac point, lies at the heart of the observation of both metallic and insulating states in bilayer graphene. In seemingly indistinguishable bilayer graphene samples, two distinct transport regimes, insulating and metallic, have been identified experimentally. Here, the authors demonstrate that these two states originate from the interplay between extended defects and evanescent modes at the Dirac point.
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Affiliation(s)
- Sam Shallcross
- Lehrstuhl für Theoretische Festkörperphysik, Staudstr. 7-B2, 91058, Erlangen, Germany.
| | - Sangeeta Sharma
- Max-Planck-Institut für Mikrostrukturphysik Weinberg 2, D-06120, Halle, Germany
| | - Heiko B Weber
- Lehrstuhl für Angewandte Physik, Staudtstr. 7, 91058, Erlangen, Germany.,Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, 91058, Germany
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14
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Konstantinidis NP. Capped carbon nanotubes with a number of ground state magnetization discontinuities increasing with their size. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:215803. [PMID: 28437255 DOI: 10.1088/1361-648x/aa6bd4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The classical ground state magnetic response of fullerene molecules that resemble capped carbon nanotubes is calculated within the framework of the antiferromagnetic Heisenberg model. It is found that the magnetic response depends subtly on spatial symmetry and chirality. Clusters based on armchair carbon nanotubes which are capped with non-neighboring pentagons and have D 5d spatial symmetry have a number of magnetization discontinuities which increases with their size. This occurs even though the model completely lacks magnetic anisotropy, and even though the only source of frustration are the two groups of six pentagons located at the ends of the molecules, which become more strongly outnumbered as the clusters are filled in the middle with more unfrustrated hexagons with increasing size. For the cluster with 180 vertices there are already seven magnetization and one susceptibility discontinuities. Contrary to that, similar molecules which have D 5h spatial symmetry reach a limit of one magnetization and two susceptibility ground state discontinuities, while fullerene molecules based on zigzag carbon nanotubes and capped by neighboring pentagons also reach a fixed number of discontinuities with increasing size.
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15
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Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene. Nat Commun 2015; 6:6419. [PMID: 25732058 PMCID: PMC4366515 DOI: 10.1038/ncomms7419] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Accepted: 01/27/2015] [Indexed: 11/08/2022] Open
Abstract
Close to charge neutrality, the electronic properties of graphene and its multilayers are sensitive to electron-electron interactions. In bilayers, for instance, interactions are predicted to open a gap between valence and conduction bands, turning the system into an insulator. In mono and (Bernal-stacked) trilayers, which remain conducting at low temperature, interactions do not have equally drastic consequences. It is expected that interaction effects become weaker for thicker multilayers, whose behaviour should converge to that of graphite. Here we show that this expectation does not correspond to reality by revealing the occurrence of an insulating state close to charge neutrality in Bernal-stacked tetralayer graphene. The phenomenology-incompatible with the behaviour expected from the single-particle band structure-resembles that observed in bilayers, but the insulating state in tetralayers is visible at higher temperature. We explain our findings, and the systematic even-odd effect of interactions in Bernal-stacked layers of different thickness that emerges from experiments, in terms of a generalization of the interaction-driven, symmetry-broken states proposed for bilayers.
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16
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Competition between spontaneous symmetry breaking and single-particle gaps in trilayer graphene. Nat Commun 2014; 5:5656. [DOI: 10.1038/ncomms6656] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2014] [Accepted: 10/23/2014] [Indexed: 11/09/2022] Open
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17
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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.
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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
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18
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Competing ordered states with filling factor two in bilayer graphene. Nat Commun 2014; 5:4550. [DOI: 10.1038/ncomms5550] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2014] [Accepted: 06/27/2014] [Indexed: 11/09/2022] Open
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19
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Tao HS, Chen YH, Lin HF, Liu HD, Liu WM. Layer anti-ferromagnetism on bilayer honeycomb lattice. Sci Rep 2014; 4:5367. [PMID: 24947369 PMCID: PMC4064339 DOI: 10.1038/srep05367] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2013] [Accepted: 05/29/2014] [Indexed: 11/09/2022] Open
Abstract
Bilayer honeycomb lattice, with inter-layer tunneling energy, has a parabolic dispersion relation, and the inter-layer hopping can cause the charge imbalance between two sublattices. Here, we investigate the metal-insulator and magnetic phase transitions on the strongly correlated bilayer honeycomb lattice by cellular dynamical mean-field theory combined with continuous time quantum Monte Carlo method. The procedures of magnetic spontaneous symmetry breaking on dimer and non-dimer sites are different, causing a novel phase transition between normal anti-ferromagnet and layer anti-ferromagnet. The whole phase diagrams about the magnetism, temperature, interaction and inter-layer hopping are obtained. Finally, we propose an experimental protocol to observe these phenomena in future optical lattice experiments.
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Affiliation(s)
- Hong-Shuai Tao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yao-Hua Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng-Fu Lin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hai-Di Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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20
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Vafek O, Murray JM, Cvetkovic V. Superconductivity on the brink of spin-charge order in a doped honeycomb bilayer. PHYSICAL REVIEW LETTERS 2014; 112:147002. [PMID: 24766005 DOI: 10.1103/physrevlett.112.147002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2013] [Indexed: 06/03/2023]
Abstract
Using a controlled weak-coupling renormalization group approach, we establish the mechanism of unconventional superconductivity in the vicinity of spin or charge ordered excitonic states for the case of electrons on the Bernal stacked bilayer honeycomb lattice. With one electron per site, this system, physically realized in bilayer graphene, is unstable towards a spontaneous symmetry breaking. Repulsive interactions favor excitonic order, such as a charge nematic and/or a layer antiferromagnet. We find that upon adding charge carriers to the system, the excitonic order is suppressed, and unconventional superconductivity appears in its place, before it is replaced by a Fermi liquid. We focus on firmly establishing this phenomenon using the renormalization group formalism within an idealized model with parabolic touching of conduction and valence bands.
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Affiliation(s)
- Oskar Vafek
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahasse, Florida 32306, USA
| | - James M Murray
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahasse, Florida 32306, USA and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Vladimir Cvetkovic
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahasse, Florida 32306, USA
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21
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Velasco J, Lee Y, Zhao Z, Jing L, Kratz P, Bockrath M, Lau CN. Transport measurement of Landau level gaps in bilayer graphene with layer polarization control. NANO LETTERS 2014; 14:1324-1328. [PMID: 24484507 DOI: 10.1021/nl4043399] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Landau level (LL) gaps are important parameters for understanding electronic interactions and symmetry-broken processes in bilayer graphene (BLG). Here we present transport spectroscopy measurements of LL gaps in double-gated suspended BLG with high mobilities in the quantum Hall regime. By using bias as a spectroscopic tool, we measure the gap Δ for the quantum Hall (QH) state at filling factors ν = ±4 and -2. The single-particle Δ(ν=4) scales linearly with magnetic field B and is independent of the out-of-plane electric field E⊥. For the symmetry-broken ν = -2 state, the measured values of Δ(ν=-2) are ∼1.1 meV/T and 0.17 meV/T for singly gated geometry and dual-gated geometry at E⊥ = 0, respectively. The difference between the two values arises from the E⊥. dependence of Δ(ν=-2), suggesting that the ν = -2 state is layer polarized. Our studies provide the first measurements of the gaps of the broken symmetry QH states in BLG with well-controlled E⊥ and establish a robust method that can be implemented for studying similar states in other layered materials.
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Affiliation(s)
- J Velasco
- Department of Physics and Astronomy, University of California, Riverside , Riverside, California 92521, United States
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22
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San-Jose P, Gorbachev RV, Geim AK, Novoselov KS, Guinea F. Stacking boundaries and transport in bilayer graphene. NANO LETTERS 2014; 14:2052-2057. [PMID: 24605877 DOI: 10.1021/nl500230a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Pristine bilayer graphene behaves in some instances as an insulator with a transport gap of a few millielectronvolts. This behavior has been interpreted as the result of an intrinsic electronic instability induced by many-body correlations. Intriguingly, however, some samples of similar mobility exhibit good metallic properties with a minimal conductivity of the order of 2e(2)/h. Here, we propose an explanation for this dichotomy, which is unrelated to electron interactions and based instead on the reversible formation of boundaries between stacking domains ("solitons"). We argue, using a numerical analysis, that the hallmark features of the previously inferred many-body insulating state can be explained by scattering on boundaries between domains with different stacking order (AB and BA). We furthermore present experimental evidence, reinforcing our interpretation, of reversible switching between a metallic and an insulating regime in suspended bilayers when subjected to thermal cycling or high current annealing.
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Affiliation(s)
- P San-Jose
- Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Cantoblanco, 28049 Madrid, Spain
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23
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Ki DK, Morpurgo AF. High-quality multiterminal suspended graphene devices. NANO LETTERS 2013; 13:5165-5170. [PMID: 24080018 DOI: 10.1021/nl402462q] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We introduce a new scheme to realize suspended, multiterminal graphene structures that can be current annealed successfully to obtain uniform, very high quality devices. A key aspect is that the bulky metallic contacts are not connected directly to the part of graphene probed by transport measurements, but only through etched constriction, which prevents the contacts from acting invasively. The device high quality and uniformity is demonstrated by a reproducibly narrow (δn ~ 10(9) cm(-2)) resistance peak around charge neutrality, by carrier mobility values exceeding 10(6) cm(2) V(-1) s(-1), by the observation of integer quantum Hall plateaus starting at 30 mT and of symmetry broken states at about 200 mT, and by the occurrence of a negative multiterminal resistance directly proving the occurrence of ballistic transport. As these multiterminal devices enable measurements that cannot be done in a simpler two-terminal configuration, we anticipate that their use in future studies of graphene-based systems will be particularly relevant.
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Affiliation(s)
- Dong-Keun Ki
- Départment de Physique de la Matiére Condensée (DPMC) and Group of Applied Physics (GAP), University of Geneva , 24 quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland
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24
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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.
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Affiliation(s)
- Edward McCann
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
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25
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Lee Y, Velasco J, Tran D, Zhang F, Bao W, Jing L, Myhro K, Smirnov D, Lau CN. Broken symmetry quantum Hall states in dual-gated ABA trilayer graphene. NANO LETTERS 2013; 13:1627-1631. [PMID: 23527578 DOI: 10.1021/nl4000757] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
ABA-stacked trilayer graphene is a unique 2D electron system with mirror reflection symmetry and unconventional quantum Hall effect. We present low-temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors ν = -8, -2, 2, 6, and 10, which is in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau level (LL). Under an out-of-plane electric field E(perpendicular), we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E(perpendicular) selectively breaks the LL degeneracies in the electron-doped or hole-doped regimes. Our results underscore the rich interaction-induced phenomena in trilayer graphene.
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Affiliation(s)
- Yongjin Lee
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, United States
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26
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Mkhitaryan VV, Mishchenko EG. Localized states due to expulsion of resonant impurity levels from the continuum in bilayer graphene. PHYSICAL REVIEW LETTERS 2013; 110:086805. [PMID: 23473187 DOI: 10.1103/physrevlett.110.086805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2012] [Indexed: 06/01/2023]
Abstract
The Anderson impurity problem is considered for a graphene bilayer subject to a gap-opening bias. In-gap localized states are produced even when the impurity level overlaps with the continuum of band electrons. The effect depends strongly on the polarity of the applied bias as long as hybridization with the impurity occurs within a single layer. For an impurity level inside the conduction band a positive bias creates the new localized in-gap state. A negative bias does not produce the same result and leads to a simple broadening of the impurity level. The implications for transport are discussed including a possibility of the gate-controlled Kondo effect.
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Affiliation(s)
- V V Mkhitaryan
- Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
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27
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Bao W, Myhro K, Zhao Z, Chen Z, Jang W, Jing L, Miao F, Zhang H, Dames C, Lau CN. In situ observation of electrostatic and thermal manipulation of suspended graphene membranes. NANO LETTERS 2012; 12:5470-5474. [PMID: 23043470 DOI: 10.1021/nl301836q] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Graphene is nature's thinnest elastic membrane, and its morphology has important impacts on its electrical, mechanical, and electromechanical properties. Here we report manipulation of the morphology of suspended graphene via electrostatic and thermal control. By measuring the out-of-plane deflection as a function of applied gate voltage and number of layers, we show that graphene adopts a parabolic profile at large gate voltages with inhomogeneous distribution of charge density and strain. Unclamped graphene sheets slide into the trench under tension; for doubly clamped devices, the results are well-accounted for by membrane deflection with effective Young's modulus E = 1.1 TPa. Upon cooling to 100 K, we observe buckling-induced ripples in the central portion and large upward buckling of the free edges, which arises from graphene's large negative thermal expansion coefficient.
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Affiliation(s)
- Wenzhong Bao
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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28
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Lang TC, Meng ZY, Scherer MM, Uebelacker S, Assaad FF, Muramatsu A, Honerkamp C, Wessel S. Antiferromagnetism in the Hubbard model on the Bernal-stacked honeycomb bilayer. PHYSICAL REVIEW LETTERS 2012; 109:126402. [PMID: 23005964 DOI: 10.1103/physrevlett.109.126402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2012] [Indexed: 06/01/2023]
Abstract
Using a combination of quantum Monte Carlo simulations, functional renormalization group calculations and mean-field theory, we study the Hubbard model on the Bernal-stacked honeycomb bilayer at half-filling as a model system for bilayer graphene. The free bands consisting of two Fermi points with quadratic dispersions lead to a finite density of states at the Fermi level, which triggers an antiferromagnetic instability that spontaneously breaks sublattice and spin rotational symmetry once local Coulomb repulsions are introduced. Our results reveal an inhomogeneous participation of the spin moments in the ordered ground state, with enhanced moments at the threefold coordinated sites. Furthermore, we find the antiferromagnetic ground state to be robust with respect to enhanced interlayer couplings and extended Coulomb interactions.
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Affiliation(s)
- Thomas C Lang
- Institute for Theoretical Solid State Physics, RWTH Aachen University, Germany.
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29
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Kharitonov M. Canted antiferromagnetic phase of the ν=0 quantum Hall state in bilayer graphene. PHYSICAL REVIEW LETTERS 2012; 109:046803. [PMID: 23006103 DOI: 10.1103/physrevlett.109.046803] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2011] [Indexed: 06/01/2023]
Abstract
Motivated to understand the nature of the strongly insulating ν=0 quantum Hall state in bilayer graphene, we develop the theory of the state in the framework of quantum Hall ferromagnetism. The generic phase diagram, obtained in the presence of the isospin anisotropy, perpendicular electric field, and Zeeman effect, consists of the spin-polarized ferromagnetic (F), canted antiferromagnetic (CAF), and partially (PLP) and fully (FLP) layer-polarized phases. We address the edge transport properties of the phases. Comparing our findings with the recent data on suspended dual-gated devices, we conclude that the insulating ν=0 state realized in bilayer graphene at lower electric field is the CAF phase. We also predict a continuous and a sharp insulator-metal phase transition upon tilting the magnetic field from the insulating CAF and FLP phases, respectively, to the F phase with metallic edge conductance 2e(2)/h, which could be within the reach of available fields and could allow one to identify and distinguish the phases experimentally.
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Affiliation(s)
- Maxim Kharitonov
- Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
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30
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Lu CK, Herbut IF. Zero modes and charged Skyrmions in graphene bilayer. PHYSICAL REVIEW LETTERS 2012; 108:266402. [PMID: 23004998 DOI: 10.1103/physrevlett.108.266402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2012] [Indexed: 06/01/2023]
Abstract
We show that the electric charge of the Skyrmion in the vector order parameters that characterize the quantum anomalous spin Hall state and the layer antiferromagnet in a graphene bilayer is four and zero, respectively. The result is based on the demonstration that a vortex configuration in two broken symmetry states in bilayer graphene with the quadratic band crossing has the number of zero modes doubled relative to the single layer. The doubling can be understood as a result of Kramers's theorem implied by the "pseudo time reversal" symmetry of the vortex Hamiltonian. Disordering the quantum anomalous spin Hall state by Skyrmion condensation should produce a superconductor of an elementary charge 4e.
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Affiliation(s)
- Chi-Ken Lu
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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31
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Ki DK, Morpurgo AF. Crossover from Coulomb blockade to quantum Hall effect in suspended graphene nanoribbons. PHYSICAL REVIEW LETTERS 2012; 108:266601. [PMID: 23004999 DOI: 10.1103/physrevlett.108.266601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2012] [Indexed: 06/01/2023]
Abstract
Suspended graphene nanoribbons formed during current annealing of suspended graphene flakes have been investigated experimentally. Transport measurements show the opening of a transport gap around charge neutrality due to the formation of "Coulomb islands", coexisting with quantum Hall conductance plateaus appearing at moderate values of the magnetic field B. Upon increasing B, the transport gap is rapidly suppressed, and is taken over by a much larger energy gap due to electronic correlations. Our observations show that suspended nanoribbons allow the investigation of phenomena that could not so far be accessed in ribbons on SiO(2) substrates.
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Affiliation(s)
- Dong-Keun Ki
- Départment de Physique de la Matiére Condensée (DPMC) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland
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32
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Evidence for a spontaneous gapped state in ultraclean bilayer graphene. Proc Natl Acad Sci U S A 2012; 109:10802-5. [PMID: 22685212 DOI: 10.1073/pnas.1205978109] [Citation(s) in RCA: 97] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
At the charge neutrality point, bilayer graphene (BLG) is strongly susceptible to electronic interactions and is expected to undergo a phase transition to a state with spontaneously broken symmetries. By systematically investigating a large number of single-and double-gated BLG devices, we observe a bimodal distribution of minimum conductivities at the charge neutrality point. Although σ(min) is often approximately 2-3 e(2)/h (where e is the electron charge and h is Planck's constant), it is several orders of magnitude smaller in BLG devices that have both high mobility and low extrinsic doping. The insulating state in the latter samples appears below a transition temperature T(c) of approximately 5 K and has a T = 0 energy gap of approximately 3 meV. Transitions between these different states can be tuned by adjusting disorder or carrier density.
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33
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Zhang F, MacDonald AH. Distinguishing spontaneous quantum Hall states in bilayer graphene. PHYSICAL REVIEW LETTERS 2012; 108:186804. [PMID: 22681103 DOI: 10.1103/physrevlett.108.186804] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2011] [Indexed: 06/01/2023]
Abstract
Chirally stacked N-layer graphene with N≥2 is susceptible to a variety of distinct broken symmetry states in which each spin-valley flavor spontaneously transfers charge between layers. In mean-field theory, one of the likely candidate ground states for a neutral bilayer is the layer antiferromagnet that has opposite spin polarizations in opposite layers. In this Letter, we analyze how the layer antiferromagnet and other competing states are influenced by Zeeman fields that couple to spin and by interlayer electric fields that couple to layer pseudospin, and comment on the possibility of using Zeeman responses and edge state signatures to identify the character of the bilayer ground state experimentally.
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Affiliation(s)
- Fan Zhang
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
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34
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Velasco J, Jing L, Bao W, Lee Y, Kratz P, Aji V, Bockrath M, Lau CN, Varma C, Stillwell R, Smirnov D, Zhang F, Jung J, MacDonald AH. Transport spectroscopy of symmetry-broken insulating states in bilayer graphene. NATURE NANOTECHNOLOGY 2012; 7:156-160. [PMID: 22266634 DOI: 10.1038/nnano.2011.251] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2011] [Accepted: 12/19/2011] [Indexed: 05/31/2023]
Abstract
Bilayer graphene is an attractive platform for studying new two-dimensional electron physics, because its flat energy bands are sensitive to out-of-plane electric fields and these bands magnify electron-electron interaction effects. Theory predicts a variety of interesting broken symmetry states when the electron density is at the carrier neutrality point, and some of these states are characterized by spontaneous mass gaps, which lead to insulating behaviour. These proposed gaps are analogous to the masses generated by broken symmetries in particle physics, and they give rise to large Berry phase effects accompanied by spontaneous quantum Hall effects. Although recent experiments have provided evidence for strong electronic correlations near the charge neutrality point, the presence of gaps remains controversial. Here, we report transport measurements in ultraclean double-gated bilayer graphene and use source-drain bias as a spectroscopic tool to resolve a gap of ∼2 meV at the charge neutrality point. The gap can be closed by a perpendicular electric field of strength ∼15 mV nm(-1), but it increases monotonically with magnetic field, with an apparent particle-hole asymmetry above the gap. These data represent the first spectroscopic mapping of the ground states in bilayer graphene in the presence of both electric and magnetic fields.
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Affiliation(s)
- J Velasco
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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