Topological phase transitions with and without energy gap closing

Abstract

Topological phase transitions in a three-dimensional (3D) topological insulator (TI) with an exchange field of strength $g$ are studied by calculating spin Chern numbers $C^{\pm }(k_z)$ with momentum $k_z$ as a parameter. When $|g|$ exceeds a critical value $g_c$, a transition of the 3D TI into a Weyl semimetal occurs, where two Weyl points appear as critical points separating $k_z$ regions with different first Chern numbers. For $|g|<g_c$, $C^{\pm }(k_z)$ undergo a transition from $\pm 1$ to 0 with increasing $|k_z|$ to a critical value $k_z^C$. Correspondingly, surface states exist for $|k_z|<k_z^C$, and vanish for $|k_z|\ge k_z^C$. The transition at $|k_z|=k_z^C$ is acompanied by closing of spin spectrum gap rather than energy gap.

5 pages, 5 figures

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Cited by in corpus (5)

• Gate tuning from exciton superfluid to quantum anomalous Hall in van der Waals heterobilayer
• The characterization of topological properties in Quantum Monte Carlo simulations of the Kane-Mele-Hubbard model
• Optimizing Topological Switching in Confined 2D-Xene Nanoribbons via Finite-Size Effects
• The scaling behavior of the insulator to plateau transition in topological band model
• Unconventional topological transitions in a self-organized magnetic ladder