Exact Landau Level Description of Geometry and Interaction in a Flatband
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.
- Authors:
-
[1];
[2];
[3];
[4];
[5]
- Flatiron Institute, New York, NY (United States)
- Flatiron Institute, New York, NY (United States); Stony Brook Univ., NY (United States)
- Flatiron Institute, New York, NY (United States); Columbia Univ., New York, NY (United States)
- Zhejiang Univ., Hangzhou (China). Zhejiang Inst. of Modern Physics
- Nanyang Technological Univ. (Singapore); Agency for Science, Technology and Research (A*STAR) (Singapore). Inst. of High Performance Computing
- Publication Date:
- Research Org.:
- Columbia Univ., New York, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); US Air Force Office of Scientific Research (AFOSR); National Key Research and Development Program of China; Singapore National Research Foundation (NRF)
- OSTI Identifier:
- 1980237
- Grant/Contract Number:
- SC0019443; FA9550-20-1-0260; 2020YFA0309200; NRF-NRFF12-2020-0005
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 127; Journal Issue: 24; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; fractional quantum Hall effect; goemetric & topological phases; Landau levels; strong interaction; bilayer films; two-dimensional electron system; band structure methods; exact diagonalization; geometry; symmetries in condensed matter
Citation Formats
Wang, Jie, Cano, Jennifer, Millis, Andrew J., Liu, Zhao, and Yang, Bo. Exact Landau Level Description of Geometry and Interaction in a Flatband. United States: N. p., 2021.
Web. doi:10.1103/physrevlett.127.246403.
Wang, Jie, Cano, Jennifer, Millis, Andrew J., Liu, Zhao, & Yang, Bo. Exact Landau Level Description of Geometry and Interaction in a Flatband. United States. https://doi.org/10.1103/physrevlett.127.246403
Wang, Jie, Cano, Jennifer, Millis, Andrew J., Liu, Zhao, and Yang, Bo. Fri .
"Exact Landau Level Description of Geometry and Interaction in a Flatband". United States. https://doi.org/10.1103/physrevlett.127.246403. https://www.osti.gov/servlets/purl/1980237.
@article{osti_1980237,
title = {Exact Landau Level Description of Geometry and Interaction in a Flatband},
author = {Wang, Jie and Cano, Jennifer and Millis, Andrew J. and Liu, Zhao and Yang, Bo},
abstractNote = {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.},
doi = {10.1103/physrevlett.127.246403},
journal = {Physical Review Letters},
number = 24,
volume = 127,
place = {United States},
year = {Fri Dec 10 00:00:00 EST 2021},
month = {Fri Dec 10 00:00:00 EST 2021}
}
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