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Xiang F, Gupta A, Chaves A, Krix ZE, Watanabe K, Taniguchi T, Fuhrer MS, Peeters FM, Neilson D, Milošević MV, Hamilton AR. Intra-Zero-Energy Landau Level Crossings in Bilayer Graphene at High Electric Fields. NANO LETTERS 2023; 23:9683-9689. [PMID: 37883804 DOI: 10.1021/acs.nanolett.3c01456] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2023]
Abstract
The highly tunable band structure of the zero-energy Landau level (zLL) of bilayer graphene makes it an ideal platform for engineering novel quantum states. However, the zero-energy Landau level at high electric fields has remained largely unexplored. Here we present magnetotransport measurements of bilayer graphene in high transverse electric fields. We observe previously undetected Landau level crossings at filling factors ν = -2, 1, and 3 at high electric fields. These crossings provide constraints for theoretical models of the zero-energy Landau level and show that the orbital, valley, and spin character of the quantum Hall states at high electric fields is very different from low electric fields. At high E, new transitions between states at ν = -2 with different orbital and spin polarization can be controlled by the gate bias, while the transitions between ν = 0 → 1 and ν = 2 → 3 show anomalous behavior.
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Affiliation(s)
- Feixiang Xiang
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Abhay Gupta
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Andrey Chaves
- Universidade Federal do Ceará, Departamento de Física, Caixa Postal 6030, 60455-760 Fortaleza, Ceará Brazil
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - Zeb E Krix
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Kenji Watanabe
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Michael S Fuhrer
- School of Physics and Astronomy and ARC Centre of Excellence in Future Low-Energy Electronics Technologies (FLEET), Monash University, Clayton, Victoria 3800, Australia
| | - François M Peeters
- Universidade Federal do Ceará, Departamento de Física, Caixa Postal 6030, 60455-760 Fortaleza, Ceará Brazil
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - David Neilson
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - Milorad V Milošević
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
- NANOlab Center of Excellence, University of Antwerp, B-2020 Antwerp, Belgium
| | - Alexander R Hamilton
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
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2
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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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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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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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5
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Li J, Tupikov Y, Watanabe K, Taniguchi T, Zhu J. Effective Landau Level Diagram of Bilayer Graphene. PHYSICAL REVIEW LETTERS 2018; 120:047701. [PMID: 29437431 DOI: 10.1103/physrevlett.120.047701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Revised: 11/18/2017] [Indexed: 06/08/2023]
Abstract
The E=0 octet of bilayer graphene in the filling factor range of -4<ν<4 is a fertile playground for many-body phenomena, yet a Landau level diagram is missing due to strong interactions and competing quantum degrees of freedom. We combine measurements and modeling to construct an empirical and quantitative spectrum. The single-particlelike diagram incorporates interaction effects effectively and provides a unified framework to understand the occupation sequence, gap energies, and phase transitions observed in the octet. It serves as a new starting point for more sophisticated calculations and experiments.
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Affiliation(s)
- Jing Li
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Yevhen Tupikov
- 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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6
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Hunt BM, Li JIA, Zibrov AA, Wang L, Taniguchi T, Watanabe K, Hone J, Dean CR, Zaletel M, Ashoori RC, Young AF. Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene. Nat Commun 2017; 8:948. [PMID: 29038518 PMCID: PMC5715057 DOI: 10.1038/s41467-017-00824-w] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2017] [Accepted: 07/28/2017] [Indexed: 11/16/2022] Open
Abstract
The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers. The phase diagram of bilayer graphene at high magnetic fields has been an outstanding question, with orders possibly between multiple internal quantum degrees of freedom. Here, Hunt et al. report the measurement of the valley and orbital order, allowing them to directly reconstruct the phase diagram.
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Affiliation(s)
- B M Hunt
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.,Department of Physics, Columbia University, New York, NY, 10027, USA.,Department of Physics, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
| | - J I A Li
- Department of Physics, Columbia University, New York, NY, 10027, USA
| | - A A Zibrov
- Department of Physics, University of California, Santa Barbara, CA, 93106, USA
| | - L Wang
- Department of Mechanical Engineering, Columbia University, New York, NY, 10027, USA
| | - T Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki, 305-0044, Japan
| | - K Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki, 305-0044, Japan
| | - J Hone
- Department of Mechanical Engineering, Columbia University, New York, NY, 10027, USA
| | - C R Dean
- Department of Physics, Columbia University, New York, NY, 10027, USA
| | - M Zaletel
- Station Q, Microsoft Research, Santa Barbara, CA, 93106-6105, USA
| | - R C Ashoori
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - A F Young
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA. .,Department of Physics, University of California, Santa Barbara, CA, 93106, USA.
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Naumis GG, Barraza-Lopez S, Oliva-Leyva M, Terrones H. Electronic and optical properties of strained graphene and other strained 2D materials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:096501. [PMID: 28540862 DOI: 10.1088/1361-6633/aa74ef] [Citation(s) in RCA: 116] [Impact Index Per Article: 16.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.
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Affiliation(s)
- Gerardo G Naumis
- Depto. de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Mexico City 01000, Mexico
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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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