Edge States in Silicene Nanodisks

TL;DR

This paper explores the electronic and topological properties of silicene nanodisks, revealing new zero-energy state counting rules, edge current behaviors, and signatures of topological phase transitions, with implications for experimental observation.

Contribution

It introduces a new counting rule for zero-energy states in silicene nanodisks and develops a low-energy theory for zigzag triangular silicene, advancing understanding of topological effects.

Findings

Helical edge currents flow around silicene nanodisks.

A new counting rule for zero-energy states is established.

Signatures of topological phase transition are identified.

Abstract

Silicene is a honeycomb-structure silicon atoms, which shares many intriguing properties with graphene. Silicene is expected to be a quantum spin-Hall insulator due to its spin-orbit interactions. We investigate the electronic properties of silicene nanodisks, which are silicene derivatives with closed edge. In case of the simplest model of graphene nanodisks, the number of the zero-energy modes is given by the lower bound of the Lieb theorem. They are standing wave states.When the spin-orbit interaction is introduced and the system becomes a topological insulator, they begin to propagate around a nanodisk. Helical edge currents flow around the edge of a nanodisk though the crystal momentum is ill-defined. We have newly 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 nanodisks with rough edge by calculating the local probability amplitude and current. Finally, the signatures of the topological phase transition in silicene nanodisks under an external electric field are revealed.Our results will be observable by means of STM experiments.