Symmetry breaking and fermionic fractional Chern insulator in topologically trivial bands

Abstract

We describe a mechanism by which fermions in topologically trivial bands can form correlated states exhibiting a fractional quantum Hall (FQH) effect upon introduction of strong repulsive interactions. These states are solid-liquid composites, in which a FQH liquid is induced by the formation of charge order (CO), following a recently proposed paradigm of symmetry-breaking topological (SBT) order [Phys. Rev. Lett. 113, 216404 (2014)]. We devise a spinless fermion model on a triangular lattice, featuring a topologically trivial phase when interactions are omitted. Adding strong short-range repulsion, we first establish a repulsion-driven CO phase at density ${\rho }_{\mathrm{CO}}=2/3$ particles per site, then dope the model to higher densities $\rho ={\rho }_{\mathrm{CO}}+\nu /6$. At $\nu =1/3,2/5$ ($\rho =13/18,11/15$), we observe definitive signatures of both CO and the FQH effect --- sharply peaked static structure factor, gapped and degenerate energy spectrum and fractionally quantized Hall conductivity ${\sigma }_{\mathrm{H}}=1/3,2/5$ in units of $e^2/h$ --- over a range of all model parameters. We thus obtain direct evidence for fermionic SBT order of FQH type in topologically trivial bands.

v2: published version

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• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
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• Higher angular momentum band inversions in two dimensions
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands
• Fractional Chern insulator states in an isolated flat band of zero Chern number
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• Combined spontaneous symmetry-breaking and symmetry-protected topological order from cluster charge interaction