Higher-Order Topological States with Cleavage-Dependent Dirac Mass

Abstract

Topological quantum chemistry based on local charge profiles lacks predictive power for the crystalline cleavage of higher-order topological insulators (HOTIs). By cleaving an obstructed atomic insulator, we discover a topological phase characterized by e/2 fractional charges localized at precisely half of the corners, while the remaining empty corners host complementary vacancies of interstice charge. These zero-energy charge-vacancies and topological corners form a spatially balanced geometry, confined separately by C2 rotation symmetry. Crucially, we demonstrate that the emergence of corner zero modes dictates that specific dangling bonds-acting as the mass of a Dirac fermion-must explicitly expose in, and subtly slope toward, the corner regions. This strict directionality is verified by the anisotropic evolution of the mass term within a (2+1)-dimensional parameter space. Moreover, we find that the topological corners acquire lower entanglement entropy compared to the bulk, a behavior opposite to that of the real-space energy distribution.