A topological insulator and helical zero mode in silicene under an inhomogeneous electric field

TLDR

Silicene, a buckled silicon monolayer, hosts Dirac electrons with strong spin–orbit coupling and its band gap can be tuned and closed by an external electric field. The authors solve the low‑energy Dirac equation to construct analytic wave functions for simple geometries, enabling the study of edge and localized states. They find that increasing the electric field drives a topological phase transition from a topological insulator to a trivial band insulator, and that locally tuning the field to its critical value creates helical zero modes that can act as quantum wires or dots, a behavior also predicted for germanene.

Abstract

Silicene is a monolayer of silicon atoms forming a two-dimensional (2D) honeycomb lattice and shares almost all the remarkable properties of graphene. The low-energy structure of silicene is described by Dirac electrons with relatively large spin–orbit interactions owing to its buckled structure. A key observation is that the band structure can be controlled by applying an electric field to a silicene sheet. In particular, the gap closes at a certain critical electric field. Examining the band structure of a silicene nanoribbon, we show that a topological phase transition occurs from a topological insulator to a band insulator with an increase of electric field. We also show that it is possible to generate helical zero modes anywhere in a silicene sheet by adjusting the electric field locally to this critical value. The region may act as a quantum wire or a quantum dot surrounded by topological and/or band insulators. We explicitly construct the wave functions for some simple geometries based on the low-energy effective Dirac theory. These results are also applicable to germanene, which is a 2D honeycomb structure of germanium.