Proposal for realizing and probing topological crystalline insulators in optical lattices

TL;DR

This paper introduces a lattice model for topological crystalline insulators with a proposed experimental scheme using ultracold atoms in optical lattices, highlighting topological phase transitions and detection methods.

Contribution

It presents a new lattice model showing topological transitions and proposes a feasible ultracold atom setup to realize and detect topological crystalline insulators.

Findings

Topological phase transitions characterized by mirror winding number.

Feasible scheme for realizing topological crystalline insulators with ultracold atoms.

Method for detecting mirror winding number via quench and time-of-flight measurements.

Abstract

We develop a lattice model which exhibits topological transitions from $Z_2$ topological insulators to mirror symmetry-protected topological crystalline insulators by introducing additional spin-orbit coupling terms. The topological phase is characterized by the mirror winding number, defined within the mirror symmetry invariant subspace, which ensures the protection of gapless edge states and zero-energy corner states under specific boundary conditions. Additionally, we propose a feasible scheme using ultracold atoms confined in a stacked hexagonal optical lattice with Raman fields to realize the two-dimensional topological crystalline insulators. Detection of the mirror winding number in these systems can be achieved by implementing a simple quench sequence and observing the evolution of the time-of-flight patterns.