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Dong J, Wang J, Ledwith PJ, Vishwanath A, Parker DE. Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe_{2}. PHYSICAL REVIEW LETTERS 2023; 131:136502. [PMID: 37832017 DOI: 10.1103/physrevlett.131.136502] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 08/25/2023] [Indexed: 10/15/2023]
Abstract
The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field is a long-standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators in zero magnetic field in twisted bilayers of MoTe_{2}, at partial filling of the topological valence band (ν=-2/3 and -3/5). We study the topological valence band at half filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram near twist angle ∼3.6°. The CFL is a non-Fermi liquid phase with metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions. These key properties stabilize the exotic zero field quantum Hall phases. Finally, we present an optical signature involving "extinguished" optical responses that detects Chern bands with ideal quantum geometry.
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Affiliation(s)
- Junkai Dong
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Jie Wang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Patrick J Ledwith
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ashvin Vishwanath
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Daniel E Parker
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Ghorashi SAA, Dunbrack A, Abouelkomsan A, Sun J, Du X, Cano J. Topological and Stacked Flat Bands in Bilayer Graphene with a Superlattice Potential. PHYSICAL REVIEW LETTERS 2023; 130:196201. [PMID: 37243639 DOI: 10.1103/physrevlett.130.196201] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Revised: 02/06/2023] [Accepted: 04/12/2023] [Indexed: 05/29/2023]
Abstract
We show that bilayer graphene in the presence of a 2D superlattice potential provides a highly tunable setup that can realize a variety of flat band phenomena. We focus on two regimes: (i) topological flat bands with nonzero Chern numbers, C, including bands with higher Chern numbers |C|>1 and (ii) an unprecedented phase consisting of a stack of nearly perfect flat bands with C=0. For realistic values of the potential and superlattice periodicity, this stack can span nearly 100 meV, encompassing nearly all of the low-energy spectrum. We further show that in the topological regime, the topological flat band has a favorable band geometry for realizing a fractional Chern insulator (FCI) and use exact diagonalization to show that the FCI is in fact the ground state at 1/3 filling. Our results provide a realistic guide for future experiments to realize a new platform for flat band phenomena.
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Affiliation(s)
| | - Aaron Dunbrack
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - Ahmed Abouelkomsan
- Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
| | - Jiacheng Sun
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - Xu Du
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - Jennifer Cano
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
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Claassen M, Xian L, Kennes DM, Rubio A. Ultra-strong spin-orbit coupling and topological moiré engineering in twisted ZrS 2 bilayers. Nat Commun 2022; 13:4915. [PMID: 35995779 PMCID: PMC9395362 DOI: 10.1038/s41467-022-31604-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 06/13/2022] [Indexed: 12/02/2022] Open
Abstract
We predict that twisted bilayers of 1T-ZrS2 realize a novel and tunable platform to engineer two-dimensional topological quantum phases dominated by strong spin-orbit interactions. At small twist angles, ZrS2 heterostructures give rise to an emergent and twist-controlled moiré Kagome lattice, combining geometric frustration and strong spin-orbit coupling to give rise to a moiré quantum spin Hall insulator with highly controllable and nearly-dispersionless bands. We devise a generic pseudo-spin theory for group-IV transition metal dichalcogenides that relies on the two-component character of the valence band maximum of the 1T structure at Γ, and study the emergence of a robust quantum anomalous Hall phase as well as possible fractional Chern insulating states from strong Coulomb repulsion at fractional fillings of the topological moiré Kagome bands. Our results establish group-IV transition metal dichalcogenide bilayers as a novel moiré platform to realize strongly-correlated topological phases in a twist-tunable setting.
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Affiliation(s)
- Martin Claassen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104, USA.
| | - Lede Xian
- Songshan Lake Materials Laboratory, 523808, Dongguan, Guangdong, China
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761, Hamburg, Germany
| | - Dante M Kennes
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761, Hamburg, Germany.
- Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056, Aachen, Germany.
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761, Hamburg, Germany.
- Center for Computational Quantum Physics, Simons Foundation Flatiron Institute, New York, NY, 10010, USA.
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Wang J, Liu Z. Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models. PHYSICAL REVIEW LETTERS 2022; 128:176403. [PMID: 35570419 DOI: 10.1103/physrevlett.128.176403] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 03/24/2022] [Indexed: 06/15/2023]
Abstract
We propose models of twisted multilayer graphene that exhibit exactly flat Bloch bands with arbitrary Chern numbers and ideal band geometries. The models are constructed by twisting two sheets of Bernal-stacked multiple graphene layers with only intersublattice couplings. Analytically we show that flatband wave functions in these models exhibit a momentum space holomorphic character, leading to ideal band geometries. We also explicitly demonstrate a generic "wave function exchange" mechanism that generates the high Chern numbers of these ideal flatbands. The ideal band geometries and high Chern numbers of the flatbands imply the possibility of hosting exotic fractional Chern insulators which do not have analogues in continuum Landau levels. We numerically verify that these exotic fractional Chern insulators are model states for short-range interactions, characterized by exact ground-state degeneracies at zero energy and infinite particle-cut entanglement gaps.
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Affiliation(s)
- Jie Wang
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Zhao Liu
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China
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Wang J, Cano J, Millis AJ, Liu Z, Yang B. Exact Landau Level Description of Geometry and Interaction in a Flatband. PHYSICAL REVIEW LETTERS 2021; 127:246403. [PMID: 34951815 DOI: 10.1103/physrevlett.127.246403] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Accepted: 10/08/2021] [Indexed: 06/14/2023]
Abstract
Flatbands appear in many condensed matter systems, including the two-dimensional electron gas in a high magnetic field, correlated materials, and moiré heterostructures. They are characterized by intrinsic geometric properties such as the Berry curvature and Fubini-Study metric. The influence of the band geometry on electron-electron interaction is difficult to understand analytically because the geometry is in general nonuniform in momentum space. In this work, we study the topological flatband of Chern number C=1 with a momentum-dependent but positive definite Berry curvature that fluctuates in sync with Fubini-Study metric. We derive an exact correspondence between such ideal flatbands and Landau levels and show that the band geometry fluctuation gives rise to a new type of interaction in the corresponding Landau levels that depends on the center of mass of two particles. We characterize such interactions by generalizing the usual Haldane pseudopotentials. This mapping gives exact zero-energy ground states for short-ranged repulsive generalized pseudopotentials in flatbands, in analogy to fractional quantum Hall systems. Driving the center-of-mass interactions beyond the repulsive regime leads to a dramatic reconstruction of the ground states towards gapless phases. The generalized pseudopotential could be a useful basis for future numerical studies.
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Affiliation(s)
- Jie Wang
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Jennifer Cano
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11974, USA
| | - Andrew J Millis
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Department of Physics, Columbia University, 538 W 120th Street, New York, New York 10027, USA
| | - Zhao Liu
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China
| | - Bo Yang
- Division of Physics and Applied Physics, Nanyang Technological University, 637371 Singapore
- Institute of High Performance Computing, A*STAR, 138632 Singapore
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Yang B, Hu ZX, Lee CH, Papić Z. Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2017; 118:146403. [PMID: 28430476 DOI: 10.1103/physrevlett.118.146403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2016] [Indexed: 06/07/2023]
Abstract
We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems that are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to expand any translation-invariant interaction over a complete basis, and directly reveals the intrinsic metric of incompressible FQH fluids. We show that purely anisotropic pseudopotentials give rise to new types of bound states for small particle clusters in the infinite plane, and can be used as a diagnostic of FQH nematic order. We also demonstrate that generalized pseudopotentials quantify the anisotropic contribution to the effective interaction potential, which can be particularly large in models of fractional Chern insulators.
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Affiliation(s)
- Bo Yang
- Complex Systems Group, Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore
| | - Zi-Xiang Hu
- Department of Physics, Chongqing University, Chongqing 401331, People's Republic of China
| | - Ching Hua Lee
- Material Science and Engineering, Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore
| | - Z Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
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