Topological Metal‐Insulator Phase Transition in A Square Lattice Model

Abstract A square lattice model with next‐nearest‐neighbor hopping and staggered fluxes is investigated, revealing distinct topological characteristics in different phases emerging at specific filling levels. Specifically, at quarter filling, the system exhibits metallic phases with Chern insulator (CI)‐like features and a topological insulator phase with polarization . At half filling, the metallic phases, CI phases, and trivial insulator phases are characterized by , , and , respectively. Notably, the half‐filled metallic phases with CI‐like features exhibit three distinct spatial distributions of boundary states, i.e., type‐I corner states confined to the corners, type‐I edge states localized along the edges but bypassing the corners, and type‐II corner states localized near the corners. The half‐filled CI phases support the existence of type‐II edge states and type‐II corner states. Moreover, a scheme is proposed to achieve coupling with arbitrary phase factors in a topolectrical circuit. The work deepens the understanding of topological states and enriches the study of phase transitions in systems with broken time‐reversal symmetry.