Topological properties of a periodically driven Creutz ladder

Abstract

We have investigated a periodically driven Creutz ladder in presence of two different driving protocols, namely, a sinusoidal drive and a δ-kick imparted to the ladder at regular intervals of time. Specifically, we have studied the topological properties corresponding to the trivial and the non-trivial limits of the static (undriven) case via computing suitable topological invariants. Corresponding to the case where the chiral symmetry of the ladder is intact, in addition to the zero energy modes, π energy modes appear in both these cases. Further, two different frequency regimes of the driving protocol emerge, where the Floquet-Magnus expansion is employed particularly to study the high frequency regime for the sinusoidal drive. Apart from the physics being identical in the high frequency and the static scenarios, the zero energy modes show distinctive features at low and high frequencies. For the sinusoidal drive, there exists a sharp frequency threshold beyond which the zero energy modes only exist in the topological limit, while in the trivial limit, it exist only upto the same threshold frequency. In presence of the δ-kick, the Creutz ladder demonstrates higher values of the topological invariant, and as a consequence, the system possesses larger number of edge modes.