Topological Phase Transitions and Evolution of Boundary States Induced by Zeeman Fields in Second-Order Topological Insulators

Abstract

Second-order topological insulators (SOTIs) are a class of materials hosting gapless bound states at boundaries with dimension lower than the bulk by two. In this work, we investigate the effect of Zeeman field on two- and three-dimensional time-reversal invariant SOTIs. We find that a diversity of topological phase transitions can be driven by the Zeeman field, including both boundary and bulk types. For boundary topological phase transitions, we find that the Zeeman field can change the time-reversal invariant SOTIs to time-reversal symmetry breaking SOTIs, accompanying with the change of the number of robust corner or hinge states. Relying on the direction of Zeeman field, the number of bound states per corner or chiral states per hinge can be either one or two in the resulting time-reversal symmetry breaking SOTIs. Remarkably, for bulk topological phase transitions, we find that the transitions can result in Chern insulator phases with chiral edge states and topological semimetal phases with sharply-localized corner states in two dimensions, and hybrid-order Weyl semimetal phases with the coexistence of surface Fermi arcs and gapless hinge states in three dimensions. Our study reveals that the Zeeman field can induce very rich physics in higher-order topological materials.