Hexagonally Warped Dirac Cones and Topological Phase Transition in Silicene Superstructure

TL;DR

This paper explores the topological properties of silicene superstructures, revealing hexagonally warped Dirac cones and confirming their quantum spin-Hall insulating phase without external electric field-induced phase transitions.

Contribution

It demonstrates the existence of hexagonally warped Dirac cones in silicene superstructures and analyzes their topological phase stability under external electric fields.

Findings

Silicene superstructure is a quantum spin-Hall insulator.

Hexagonally warped Dirac cones are observed due to Coulomb interaction.

No topological phase transition occurs under external electric field.

Abstract

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice. We investigate the topological properties of a silicene superstructure generated by an external periodic potential. The superstructure is a quantum spin-Hall (QSH) insulator if it is topologically connected to silicene. It is remarkable that two inequivalent K and K' points in the silicene Brillouin zone are identified in certain superstructures. In such a case two Dirac cones coexist at the same Dirac point in the momentum space and they are hexagonally warped by the Coulomb interaction. We carry out a numerical analysis by taking an instance of the ($3\times 3$) superstructure on the ($4\times 4$) structure of the Ag substrate. We show that it is a QSH insulator, that there exists no topological phase transition by external electric field, and that the hexagonally warping occurs in the band structure.