Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators

Abstract

The quantum metric of single-particle wave functions in topological flatbands plays a crucial role in determining the stability of fractional Chern insulating (FCI) states. Here, we unravel that the quantum metric causes the many-body Chern number of the FCI states to deviate sharply from the expected value associated with partial filling of the single-particle topological flatband. Furthermore, the variation of the quantum metric in momentum space induces band dispersion through interactions, affecting the stability of the FCI states. This causes a reentrant transition into the Fermi liquid from the FCI phase as the interaction strength increases.

18 pages, 10 figures

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• Enhanced Kohn-Luttinger topological superconductivity in bands with nontrivial geometry
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• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Geometric transport signatures of strained multi-Weyl semimetals
• Unconventional Fractional Phases in Multi-Band Vortexable Systems