Engineering topological flat bands in $\Gamma$-valley moir\'e systems with Ising-type SOC: twisted 1T-ZrS$_2$ and 1T-SnSe$_2$

Abstract

Twisted moir\'e superlattices hosting topological flat bands provide a platform to explore the interplay between topology and correlations. Here we investigate topological band structures in $\Gamma$-valley moir\'e systems based on 1T-ZrS$_2$ and 1T-SnSe$_2$. Using large-scale ab initio calculations and continuum modelling, we demonstrate that both materials exhibit an approximate spin-$U(1)$ symmetry and host isolated topological moir\'e valence bands, including quantum spin Hall and high spin Chern states. By constructing a hierarchy of $\Gamma$-valley moir\'e continuum models, we show that isolated moir\'e bands carry a trivial $C_3$ symmetry indicator when the low-energy physics is described by a single effective orbital and a single layer-hybridized branch, either bonding or antibonding. Topological bands therefore arise from inter-branch and/or inter-orbital coupling. Moreover, we determine interaction-driven phase diagrams using Hartree--Fock and exact diagonalization, finding various phases tunable by twist angle, interaction strength, and displacement field. We identify specific conditions under which fractional Chern insulators are favored. Together with previous work showing that the moir\'e conduction bands of 1T-ZrS$_2$ and 1T-SnSe$_2$ realize $M$-valley twisting and host quasi-one-dimensional physics, our results establish these systems as ideal platforms for strongly correlated moir\'e physics and provide a systematic framework for understanding topological band structures in $\Gamma$-valley moir\'e materials.