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Title: Exact landau level description of geometry and interaction in a flatband
Authors: Wang, Jie
Cano, Jennifer
Millis, Andrew J.
Liu, Zhao
Yang, Bo
Keywords: Science::Physics
Issue Date: 2021
Source: Wang, J., Cano, J., Millis, A. J., Liu, Z. & Yang, B. (2021). Exact landau level description of geometry and interaction in a flatband. Physical Review Letters, 127(24), 246403-.
Project: NRF-NRFF12-2020-0005
NTU SUG grant 
Journal: Physical Review Letters 
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.
ISSN: 0031-9007
DOI: 10.1103/PhysRevLett.127.246403
Rights: © 2021 American Physical Society. All rights reserved. This paper was published in Physical Review Letters and is made available with permission of American Physical Society.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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