A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order

TL;DR

This paper investigates the effects of strong short-range interactions in ideal Chern bands, revealing novel ground states, phases like metallic and superconducting, and providing analytical tools for understanding topological order in correlated materials.

Contribution

It introduces the 'three-rule' for flatband wave functions, develops a variational approach to identify phases, and connects these findings to frustration-free models and topological order.

Findings

Discovery of a non-trivial ground state manifold in fractional Chern bands

Identification of conditions leading to metallic and superconducting phases

Analytical expression for the off-diagonal long-range order correlator

Abstract

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 non-trivial ground state manifold within the band filling range $0 < \nu < 1$ and introduce a general principle, the ''three-rule'', for combining flatband 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 non-trivial 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 non-commuting projector Hamiltonians, potentially aiding the future construction of exact ground states for various fractional fillings.