Topological phases and phase transitions on the square-octagon lattice

TL;DR

This paper explores topological phases and phase transitions in a fermionic tight-binding model on the square-octagon lattice, revealing new Z_2 insulators and phase transitions influenced by spin-orbit coupling and gauge fields.

Contribution

It introduces a new exactly solvable model of Z_2 topological insulators on the square-octagon lattice with analysis of phase stability and transitions.

Findings

Realization of time-reversal symmetric Z_2 topological insulators

Identification of additional insulating and gapless phases

Topological phase transitions involving Fermi surface changes

Abstract

We theoretically investigate a tight binding model of fermions hopping on the square-octagon lattice which consists of a square lattice with plaquette corners themselves decorated by squares. Upon the inclusion of second neighbor spin-orbit coupling or non-Abelian gauge fields, time-reversal symmetric topological Z_2 band insulators are realized. Additional insulating and gapless phases are also realized via the non-Abelian gauge fields. Some of the phase transitions involve topological changes to the Fermi surface. The stability of the topological phases to various symmetry breaking terms is investigated via the entanglement spectrum. Our results enlarge the number of known exactly solvable models of Z_2 band insulators, and are potentially relevant to the realization and identification of topological phases in both the solid state and cold atomic gases.