Creating anomalous Floquet Chern insulators with magnetic quantum walks

TL;DR

This paper introduces a method to create anomalous Floquet Chern insulators using quantum walks of spin-1/2 particles, revealing flat bands with nonzero Chern numbers and topologically protected edge modes, with a proposed implementation using neutral atoms.

Contribution

It presents a realistic scheme to realize Floquet topological insulators via quantum walks and introduces the RLBL invariant for full topological characterization.

Findings

Nearly flat energy bands with nonzero Chern numbers

Topologically protected edge modes at boundaries

Implementation with neutral atoms in optical lattices

Abstract

We propose a realistic scheme to construct anomalous Floquet Chern topological insulators using spin-1/2 particles carrying out a discrete-time quantum walk in a two-dimensional lattice. By Floquet engineering the quantum-walk protocol, an Aharonov-Bohm geometric phase is imprinted onto closed-loop paths in the lattice, thus realizing an abelian gauge field---the analog of a magnetic flux threading a two-dimensional electron gas. We show that in the strong field regime, when the flux per plaquette is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands featuring nonvanishing Chern numbers. Furthermore, we find that because of the nonperturbative nature of the periodic driving, a second topological number---the so-called RLBL invariant---is necessary to fully characterize the anomalous Floquet topological phases of magnetic quantum walks and to compute the number of topologically protected edge modes expected at the boundaries between different phases. In the second part of this article, we discuss an implementation of this scheme using neutral atoms in two-dimensional spin-dependent optical lattices, which enables the generation of arbitrary magnetic-field landscapes, including those with sharp boundaries. The robust atom transport, which is observed along boundaries separating regions of different field strength, reveals the topological character of the Floquet Chern bands.