1
|
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.
Collapse
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.
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
Propagation of superconducting coherence via chiral quantum-Hall edge channels. Sci Rep 2017; 7:10953. [PMID: 28887486 PMCID: PMC5591196 DOI: 10.1038/s41598-017-11209-w] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2017] [Accepted: 08/21/2017] [Indexed: 11/25/2022] Open
Abstract
Recently, there has been significant interest in superconducting coherence via chiral quantum-Hall (QH) edge channels at an interface between a two-dimensional normal conductor and a superconductor (N–S) in a strong transverse magnetic field. In the field range where the superconductivity and the QH state coexist, the coherent confinement of electron- and hole-like quasiparticles by the interplay of Andreev reflection and the QH effect leads to the formation of Andreev edge states (AES) along the N–S interface. Here, we report the electrical conductance characteristics via the AES formed in graphene–superconductor hybrid systems in a three-terminal configuration. This measurement configuration, involving the QH edge states outside a graphene–S interface, allows the detection of the longitudinal and QH conductance separately, excluding the bulk contribution. Convincing evidence for the superconducting coherence and its propagation via the chiral QH edge channels is provided by the conductance enhancement on both the upstream and the downstream sides of the superconducting electrode as well as in bias spectroscopy results below the superconducting critical temperature. Propagation of superconducting coherence via QH edge states was more evident as more edge channels participate in the Andreev process for high filling factors with reduced valley-mixing scattering.
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
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
|
6
|
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
|
7
|
Maher P, Wang L, Gao Y, Forsythe C, Taniguchi T, Watanabe K, Abanin D, Papić Z, Cadden-Zimansky P, Hone J, Kim P, Dean CR. Tunable fractional quantum Hall phases in bilayer graphene. Science 2014; 345:61-4. [DOI: 10.1126/science.1252875] [Citation(s) in RCA: 122] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Symmetry-breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field, electron interactions can cause spontaneous symmetry-breaking within the spin and valley degrees of freedom, resulting in quantum Hall effect (QHE) states with complex order. Here, we report fractional QHE states in BLG that show phase transitions that can be tuned by a transverse electric field. This result provides a model platform with which to study the role of symmetry-breaking in emergent states with topological order.
Collapse
|