Spin-valley optical selection rule and strong circular dichroism in silicene

Silicene (a monolayer of silicon atoms) is a topological insulator which undergoes a topological phase transition to a band insulator under an external electric field. We propose a way of detecting the topological phase transition by way of optical absorption. We demonstrate that silicene exhibits a strong circular dichroism with respect to optical absorption and obeys a certain spin-valley selection rule. The selection rule is drastically different between the topological and trivial sectors because a band inversion takes place at the phase transition point. Hence the circular dichroism can be used as a signal to distinguish the topological and trivial sectors. Furthermore, the selection rule enables us to excite electrons with definite spin and valley indices by optical absorption. Photoinduced current is spin polarized, where the spin direction is different between the topological and band insulators. It is useful for future spintronics applications.