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The role of band geometry in fractional quantum Hall states in flat Chern bands

ORAL · Invited

Abstract

Band geometry provides a convenient way to characterize the suitability of a flat Chern band for hosting topological states. The suitability can be cast in terms of the level of saturation of a set of inequalities that are obeyed by all Chern bands. The level of saturation of these inequalities measures how similar a band is to the lowest Landau level in its ability to host fractional quantum Hall states. They along with some other conditions also measure how closely the density operators projected to the band obey the W infinity algebra.

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Publication: Stability of fractional Chern insulators with a non-Landau level continuum limit, B. Andrews, M. Raja, N. Mishra, M. P. Zaletel, R. Roy, Phys. Rev. B 109, 245111 (2023)<br>Fractional Chern insulators with a non-Landau level continuum limit, D. Bauer, S. Talkington, F. Harper, B. Andrews, and R. Roy, Phys. Rev. B 105, 045144 (2022).<br>Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model, D. Bauer, T. S. Jackson and R. Roy, Phys. Rev. B 93, 235133 (2016).<br>Geometric stability of topological lattice phases, T. S. Jackson, G. Mo ̈ller and R. Roy, Nat. Commun. 6, 8629 (2015).<br>Band geometry of fractional topological insulators, R. Roy, Phys. Rev. B 90, 075104 (2014).<br>Fractional quantum Hall physics in topological flat bands, S. A. Parameswaran, R. Roy and S. L. Sondhi, C. R. Physique 14, 816 (2013).

Presenters

  • Rahul Roy

    University of California, Los Angeles

Authors

  • Rahul Roy

    University of California, Los Angeles