Ideal Chern bands with strong short-range repulsion: Applications to correlated metals, superconductivity, and topological order

Motivated by recent experiments on correlated van der Waals materials, including twisted and rhombohedral graphene and twisted WSe_{2}, we perform an analytical and numerical study of the effects of strong on-site and short-range interactions in fractionally filled ideal Chern bands. We uncover an e...

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Bibliographic Details
Main Authors: Patrick H. Wilhelm, Andreas M. Läuchli, Mathias S. Scheurer
Format: Article
Language:English
Published: American Physical Society 2024-12-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.6.043240
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Summary:Motivated by recent experiments on correlated van der Waals materials, including twisted and rhombohedral graphene and twisted WSe_{2}, we perform an analytical and numerical study of the effects of strong on-site and short-range interactions in fractionally filled ideal Chern bands. We uncover an extensive nontrivial ground state manifold within the band filling range 0<ν<1 and introduce a general principle, the “three-rule,” for combining flat band wave functions, which governs their zero-energy property on the torus geometry. Based on the structure of these wave functions, we develop a variational approach that reveals distinct phases under different perturbations: metallic behavior emerges from a finite dispersion, and superconductivity is induced by attractive Cooper channel interactions. Our approach, not reliant on the commonly applied mean-field approximations, provides an analytical expression for the macroscopic wave function of the off-diagonal long-range order correlator, attributing pairing susceptibility to the set of nontrivial zero-energy ground state wave functions. Extending to finite screening lengths and beyond the ideal limit using exact diagonalization simulations, we demonstrate the peculiar structure in the many-body wave function's coefficients to be imprinted in the low-energy spectrum of the topologically ordered Halperin spin-singlet state. Our findings also make connections to frustration-free models of noncommuting projector Hamiltonians, potentially aiding the future construction of exact ground states for various fractional fillings.
ISSN:2643-1564