Topological Insulator and Helical Zero Mode in Silicene under Inhomogeneous Electric Field

TL;DR

This paper explores how inhomogeneous electric fields can induce topological phase transitions and generate helical zero modes in silicene, enabling the creation of quantum wires or dots in a tunable two-dimensional material.

Contribution

It demonstrates the controllability of silicene's topological phases and zero modes via local electric fields, providing a theoretical framework for quantum device design.

Findings

Topological phase transition from topological insulator to band insulator with increasing electric field.

Helical zero modes can be generated locally by tuning electric fields.

Wave functions for zero modes are explicitly constructed using Dirac theory.

Abstract

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying the 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 demonstrate that a topological phase transition occurs from a topological insulator to a band insulator with the increase of the 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 applicable also to germanene, that is a two-dimensional honeycomb structure of germanium.