Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices

TL;DR

This paper proposes a method to realize a two-dimensional higher-order topological insulator using ultracold atoms in optical lattices with orbital angular momentum, revealing corner states linked to bulk topology.

Contribution

It introduces a novel scheme to create and analyze second-order topological insulators with ultracold atoms and orbital angular momentum in optical lattices.

Findings

Topologically non-trivial regimes are accessible with feasible experimental parameters.

Corner states are characterized by Zak's phases of edge bands.

System exhibits decoupled lattice models with edge and corner states.

Abstract

We propose a realization of a two-dimensional higher-order topological insulator with ultracold atoms loaded into orbital angular momentum (OAM) states of an optical lattice. The symmetries of the OAM states induce relative phases in the tunneling amplitudes that allow to describe the system in terms of two decoupled lattice models. Each of these models displays one-dimensional edge states and zero-dimensional corner states that are correlated with the topological properties of the bulk. We show that the topologically non-trivial regime can be explored in a wide range of experimentally feasible values of the parameters of the physical system. Furthermore, we propose an alternative way to characterize the second-order topological corner states based on the computation of the Zak's phases of the bands of first-order edge states.