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.

Theoretical studies of magneto-optical Kerr and Faraday effects in two-dimensional second-order topological insulators

“…In the absence of magnetization, model Hamiltonian (1) describes a second-order topological phase ( ν = 1) 9,13,47,48 when 0 < M < 8B and a topologically trivial phase ( ν = 0 ) otherwise. An introduction of magnetization may affect the topological behaviors of the system, thereby inducing a Chern insulating phase 49,50 . The energy dispersions of Hamiltonian (1) are given by with the band index µ = 1, 2, 3, 4 .…”

Electronic structures and Aharonov–Bohm effect in higher-order topological Dirac Semimetal nanoribbons with strong confinements

“…For example, hinge or corner states are predicted to emerge in topological systems with particular symmetries such as time-reversal and fourfold rotation symmetries [13,14], spacetime-inversion symmetry [15,16], and chiral symmetry [17]. In addition, HO topological insulating phases can also be generated and modulated by external means including the Zeeman field [18,19], the stacking of antiferromagnetic TI multilayers [20], and even structural [21,22] or impurity/defect [23,24] disorders. Similar to the developing routine of the first-order topological materials, HO topology classification is also broadened from insulators to metals.…”

Topological phases and tunable Majorana zero modes in Rashba superconducting systems in the presence of Zeeman field

“…In view of the above, we systematically investigate the topological phases in two types of Rashba superconducting systems in the presence of an out-of-plane Zeeman field: a long superconducting stripe and a mesoscopic superconducting square loop. It is noted that we focus on the Zeeman field generated by exchange interaction in a quantum material and then neglect the orbital effect of the field [40]. In practical settings, the exchange field can be included by depositing the high-temperature superconducting film on a magnetic substrate.…”