Reentrant quantum spin Hall effect in the presence of an exchange field

Driven by various physical origins, the interesting reentrant phenomena in quantum Hall effect (QHE), quantum anomalous Hall effect (QAHE), and non-Hermitian systems have been discussed recently. Here, we present that the reentrant phenomena of the quantum spin Hall effect (QSHE) can be achieved by introducing a uniform exchange field into a topological insulator with a four-band model Hamiltonian. Furthermore, it is found that both time-reversal (TR) symmetry broken QSHE and spin-polarized QAHE can simultaneously be generated in the system with proper exchange field strength by inspecting the corresponding edge states. Through analyzing the energy-dependent spin-Chern number nu s and transmission in the presence of random disorders, we verify the topological protection and the robustness of induced QSHE and QAHE. Finally, the theoretical realization of reentrant QSHE in a topolectrical circuit is demonstrated. Our work not only extends the reentrant phenomena into the QSHE but also stimulates interest in their realization in different systems.

Automated summary

Recently, the interesting reentrant phenomena in quantum Hall effect (QHE), quantum anomalous Hall effect (QAHE), and non-Hermitian systems have been discussed. In this study, the reentrant phenomena in quantum spin Hall effect (QSHE) are achieved by introducing a uniform exchange field into a topological insulator with a four-band model Hamiltonian. Both time-reversal symmetry broken QSHE and spin-polarized QAHE are simultaneously generated in the system with proper exchange field strength. The topological protection and robustness of induced QSHE and QAHE are verified through analyzing the spin-Chern number and transmission in the presence of random disorders. Furthermore, the theoretical realization of reentrant QSHE in a topolectrical circuit is demonstrated.