Band mixing and particle-hole asymmetry in moir\'e fractional Chern insulators

Abstract

We investigate the effect of remote band mixing on the stability of fractional Chern insulators in a family of models that approximate continuum descriptions of moir\'e materials. Our results suggest that the experimentally observed asymmetry between filling fractions $\nu=1/3$ and $\nu=2/3$ in twisted MoTe$_2$ originates from a competition between a fractional Chern insulator, an electron Wigner crystal, and a hole Wigner crystal. In the absence of band mixing, the leading instability at $\nu = 1/3$ is the electron crystal, whereas at $\nu = 2/3$ the main competing phase is the hole crystal. Remote band mixing substantially lowers the energy of the electron crystal but has only a weak effect on the hole crystal. Consequently, it destabilizes the fractional Chern insulator at $\nu=1/3$ more strongly than at $\nu=2/3$. This mechanism also provides an explanation for the emergence of re-entrant integer quantum anomalous Hall states in moir\'e MoTe$_2$ for fillings $\nu>1/2$.