Quasi-Topological Insulator and Trigonal Warping in Gated Bilayer Silicene

TL;DR

This paper explores the topological properties and electric field controllability of bilayer silicene, revealing its quasi-topological insulator behavior, phase transitions, and the effects of trigonal warping on its electronic structure.

Contribution

It demonstrates that bilayer silicene exhibits quasi-topological insulator characteristics and identifies multiple critical electric fields affecting its band structure.

Findings

Bilayer silicene is a quasi-topological insulator with edge modes.

Electric field induces phase transitions from quasi-topological to band insulator.

Trigonal warping causes multiple gap-closing points at critical fields.

Abstract

Bilayer silicene has richer physical properties than bilayer graphene due to its buckled structure together with its trigonal symmetric structure. The buckled structure arises from a large ionic radius of silicon, and the trigonal symmetry from a particular way of hopping between two silicenes. It is a topologically trivial insulator since it carries a trivial $\mathbb{Z}_{2}$ topological charge. Nevertheless, its physical properties are more akin to those of a topological insulator than those of a band insulator. Indeed, a bilayer silicene nanoribbon has edge modes which are almost gapless and helical. We may call it a quasi-topological insulator. An important observation is that the band structure is controllable by applying the electric field to a bilayer silicene sheet. We investigate the energy spectrum of bilayer silicene under electric field. Just as monolayer silicene undergoes a phase transition from a topological insulator to a band insulator at a certain electric field, bilayer silicene makes a transition from a quasi-topological insulator to a band insulator beyond a certain critical field. Bilayer silicene is a metal while monolayer silicene is a semimetal at the critical field. Furthermore we find that there are several critical electric fields where the gap closes due to the trigonal warping effect in bilayer silicene.