Charge-ordered states in twisted MoTe$_2$

Abstract

We analyze interaction-driven charge-density-wave (CDW) states in the spin-valley polarized first valence miniband of twisted MoTe$_2$ (tMoTe$_2$) using an adiabatic mapping from the continuum model to an effective Landau-level (LL) problem. When projected to the lowest LL, the leading spatial harmonic of the moir\'e-periodic potential changes sign at a magic twist angle $\theta_c$ where the band reaches its minimum bandwidth. By solving self-consistent Hartree-Fock equations in a multi-LL Hilbert space, we find that triangular-lattice CDW states with density maxima on MX (or XM) sites or on MM sites are favored on opposite sides of the magic angle at most filling factors and that stripe order appears near $\nu_h=1/2$. We show that CDW states at $\nu_h >1/2$ can carry a nonzero total Chern number, providing a natural route to reentrant integer quantum Hall effects and discuss the energy competition between fractional Chern insulator and CDW states.