Topological Insulators on the Lieb and Perovskite Lattices

TL;DR

This paper demonstrates that electrons on Lieb and perovskite lattices can form topologically non-trivial insulators with unique spectral features when spin-orbit coupling is included, revealing new insights into lattice topology effects.

Contribution

It introduces simple lattice models with cubic symmetry that exhibit topological insulating phases and unique spectral properties, including dispersionless bands and a single Dirac cone.

Findings

Topological insulators are realized on Lieb and perovskite lattices with spin-orbit coupling.

The models show a Dirac-like spectrum with a dispersionless band at the spectrum center.

A single Dirac cone appears per Brillouin zone, indicating novel topological features.

Abstract

Electrons hopping on the sites of a two-dimensional Lieb lattice and three-dimensional edge centered cubic (perovskite) lattice are shown to form topologically non-trivial insulating phases when spin-orbit coupling is introduced. These simple models on lattices with cubic symmetry show a Dirac-like structure in the excitation spectrum but with the unusual feature that there is a dispersionless band through the center of the spectrum and only a single Dirac cone per Brillouin zone.