Topological flat bands in optical checkerboard-like lattices

TL;DR

This paper introduces simple 2D and 3D optical checkerboard lattices with tunable topological phases, including insulating, semi-metallic, and trivial states, featuring observable flat surface bands without requiring spin-orbit coupling.

Contribution

It proposes a new class of optical lattices that realize various topological phases and surface flat bands through simple parameter tuning, avoiding complex gauge fields.

Findings

Lattices can host topological insulating, semi-metallic, or trivial phases.

Surface flat bands with short localization lengths are observable.

No need for spin-orbit coupling or non-Abelian gauge fields.

Abstract

We present comparatively simple two-dimensional and three-dimensional checkerboard-like optical lattices possessing nontrivial topological properties. By simple tuning of the parameters these lattices can have a topological insulating phase, a topological semi-metallic phase, or a trivial insulating phase. This allows study of different topological phase transitions within a single cold atom system. In the topologically nontrivial phases flat bands appear at the surfaces of the system. These surface states possess short localization lengths such that they are observable even in systems with small lattice dimensions. Our proposed lattices neither need spin-orbit coupling nor non-Abelian gauge fields to reach topologically nontrivial states.