Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder

TL;DR

This paper demonstrates how periodic driving of a spinful Creutz ladder can produce rich Floquet topological phases with fourfold-degenerate edge states and large even-integer topological invariants, which can be experimentally probed.

Contribution

It introduces a method to realize Floquet topological phases with fourfold degeneracy and large invariants in a spinful Creutz ladder, expanding the understanding of Floquet topological matter.

Findings

Multiple quartets of topological edge states with quasienergies zero and π are observed.

Topological invariants (w0,wπ) can be arbitrarily large and determine edge state numbers.

A measurement scheme for detecting topological phases via generalized mean chiral displacement is proposed.

Abstract

Floquet engineering has the advantage of generating new phases with large topological invariants and many edge states by simple driving protocols. In this work, we propose an approach to obtain Floquet edge states with fourfold degeneracy and even-integer topological characterizations in a spinful Creutz ladder model, which is realizable in current experiments. Putting the ladder under periodic quenches, we found rich Floquet topological phases in the system, which belong to the symmetry class CII. Each of these phases is characterized by a pair of even integer topological invariants $(w_{0},w_{\pi}) \in 2\mathbb{Z} \times 2 \mathbb{Z}$, which can take arbitrarily large values with the increase of driving parameters. Under the open boundary condition, we further obtain multiple quartets of topological edge states with quasienergies zero and $\pi$ in the system. Their numbers are determined by the bulk topological invariants $(w_{0},w_{\pi})$ due to the bulk-edge correspondence. Finally, we propose a way to dynamically probe the Floquet topological phases in our system by measuring a generalized mean chiral displacement. Our findings thus enrich the family of Floquet topological matter, and put forward the detection of their topological properties.