Edge states in silicene nanodisks

Abstract

Silicene is a honeycomb structure of silicon atoms which shares many intriguing properties with graphene. We investigate the electronic properties of a silicene nanodisk, which is silicene with a closed edge. In the case of a graphene nanodisk, the number of the zero-energy modes is given by the lower bound of the inequality in a bipartite system, ${\ensuremath{\xi}}_{0}\ensuremath{\ge}2|{N}_{A}\ensuremath{-}{N}_{B}|$, where ${\ensuremath{\xi}}_{0}$ is the number of zero-energy modes and ${N}_{A/B}$ is the number of sites in a $A/B$ sublattice. They are standing wave states. In the case of a silicene nanodisk, they propagate around a nanodisk as a helical current, because silicene is a topological insulator due to the spin-orbit interaction. We have found the counting rule of the zero-energy states and constructed the low-energy theory of zigzag triangular silicene. We also show the validity of the bulk-edge correspondence in a nanodisk with a rough edge by calculating the local probability amplitude and current. Finally, the signatures of the topological phase transition induced by an external electric field are discussed. Our results will be observable by means of scanning tunneling microscopy experiments.