Spin-valley polarized edge states and quantum anomalous Hall states controlled by side potential in 2D honeycomb lattices

Abstract: Based on the tight-binding formalism, we study the effect of side potential on the spin and valley related electronic property of $2$D honeycomb lattices with intrinsic spin-orbit coupling, such as silicene and germanene. The side potential is composed of potential field and exchange field applied on the boundaries of the zigzag nanoribbon. It is found that the side potential could greatly affect the helical edge states with different spin indices and the spin and valley are locked to each other. By adjusting the side potential and ribbon width, the system shows quantum spin-valley Hall effect, valley polarized quantum spin Hall effect, and spin polarized quantum anomalous Hall effect. Due to the side potential and the coupling of edge states in narrow ribbon, a band gap could be opened for specific spin and the time-reversal symmetry could be broken, leading to a spin polarized quantum anomalous Hall phase. Various kinds of spin-valley polarized edge states are formed at the two boundaries. Furthermore, the spin-valley polarized insulating states can be used to realize a perfect spin-valley switch.