Intrinsic Moiré Higher-Order Topology Beyond Effective Moiré Lattice Models

Abstract: Moir\'e superlattices provide a compelling platform for exploring exotic correlated physics. Electronic interference within these systems often results in flat bands with localized electrons, which are typically described by effective moir\'e lattice models. While conventional models treat moir\'e sites as indivisible, analogous to atoms in a crystal, this picture overlooks a crucial distinction: unlike a true atom, a moir\'e site is composed of tens to thousands of atoms and is therefore spatially divisible. Here, we introduce a universal mechanism rooted in this spatial divisibility to create topological boundary states in moir\'e materials. Through tight-binding and density functional theory calculations, we demonstrate that cutting a moir\'e site with a physical boundary induces bulk topological polarization, generating robust boundary states with fractional charges. We further show that when the net edge polarization is canceled, this mechanism drives the system into an intrinsic moir\'e higher-order topological insulator (mHOTI) phase. As a concrete realization, we predict that twisted bilayer tungsten disulfide ($WS_2$) is a robust mHOTI with experimentally detectable corner states when its boundaries cut through moir\'e hole sites. Our findings generalize the theoretical framework of moir\'e higher-order topology, highlight the critical role of edge terminations, and suggest new opportunities for realizing correlated HOTIs and higher-order superconductivity in moir\'e platforms.