Topological states in two-dimensional optical lattices

TL;DR

This paper analyzes how two-dimensional optical lattices with cold atoms can host topologically non-trivial insulating states, exploring their properties, transitions, and experimental detection methods.

Contribution

It provides a comprehensive framework for realizing and identifying topological states in cold-atom optical lattices, including finite-size effects and edge state behavior.

Findings

Identification of key ingredients for topological states in optical lattices

Analysis of edge state behavior for different boundary conditions

Proposal for experimental detection via light Bragg scattering

Abstract

We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial topological character and argue that such states can be realized within a large family of realistic optical lattice Hamiltonians with cold atoms. We focus our quantitative analysis on the properties of topological states with broken time-reversal symmetry specific to cold-atom settings. In particular, we analyze finite-size effects, multi-orbital phenomena that give rise to a variety of distinct topological states and transitions between them, the dependence on the trap geometry, and most importantly, the behavior of the edge states for different types of soft and hard boundaries. Furthermore, we demonstrate the possibility of experimentally detecting the topological states through light Bragg scattering of the edge and bulk states.