Zeeman-field-induced valley-dependent topological phase transitions on the surface of a topological crystalline insulator SnTe

Mirror-symmetric (001) surfaces of a topological crystalline insulator SnTe host an even number of Dirac cone structures of surface states. A Zeeman field generically gaps the surface states, leading to a 2D topological insulator. By symmetry analysis and calculation of spin-Chern numbers, we show that with varying the direction of the Zeeman field, the system displays a rich phase diagram, consisting of a quantum anomalous Hall (QAH) phase with Chern number C = 2, a QAH phase with C = 1, a quantum pseudospin Hall phase, and an unusual insulator phase. In the QAH phase with C = 1 and the insulator phase, the two valleys X and Y are in different topological states. These valley-dependent topological phases provide a new pathway to potential applications of valleytronics.