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  • Letter
  • Open Access

Ideal Chern bands as Landau levels in curved space

Benoit Estienne1, Nicolas Regnault2,3, and Valentin Crépel4

  • 1Sorbonne Université, CNRS, Laboratoire de Physique Théorique et Hautes Énergies, LPTHE, F-75005 Paris, France
  • 2Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005 Paris, France
  • 3Department of Physics, Columbia University, New York, New York 10027, USA
  • 4Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA

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Phys. Rev. Research 5, L032048 – Published 29 September, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032048

Abstract

We prove that all the criteria proposed in the literature to identify a Chern band hosting exact fractional Chern insulating ground states, in fact, describe an equivalence with a lowest Landau level defined in curved space under a nonuniform magnetic field. In addition, we design an operational test for the most general instance of such lowest Landau-level mapping, which only relies on the computationally inexpensive evaluation of Bloch wavefunctions' derivatives. Our work clarifies the common origin of various Chern-idealness criteria, proves that these criteria exhaust all possible lowest Landau levels, and hints at classes of Chern bands that may possess interesting phases beyond Landaulevel physics.

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References (53)

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Outline

Information

Phys. Rev. Research 5, L032048– Published 29 September, 2023
  • Received 4 April 2023
  • Revised 27 July 2023
  • Accepted 11 September 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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