Topological band insulators are noninteracting lattice systems that host protected excitations at their boundaries, whose number is predicted by topological invariants of the bulk Hamiltonian. A quasi-one-dimensional system, i.e., a wire, can only be topological insulator in the presence of particle-hole symmetry or chiral symmetry. The simplest model for such a system is the Su-Schrieffer-Heeger model for polyacetylene. In this talk I will show how the theory of chiral symmetric one-dimensional topological insulators can be generalized to periodically driven quantum wires. The topologically protected steady states these wires host are steady states, eigenstates of the unitary timestep operator U, whose quasienergy is fixed by chiral symmetry of the drive sequence. The corresponding bulk topological invariants, however, cannot be derived from the effective Hamiltonian of the bulk: more detailed information about how the timestep is performed is required (as in other periodically driven systems).

As a concrete example, we illustrate our results on the periodically driven Su-Schrieffer-Heeger (SSH) model, where we give a direct visual interpretation of the novel topological invariants. If the hopping amplitudes are real, the end states here are Floquet Majorana fermions. We show that the periodically driven Su-Schrieffer-Heeger model is a continuous-time lattice realization of a broad class of discrete-time quantum walks. This allows us to also check our results against the known invariants of these walks.


Seminar, July 23, 2014, 15:00. Seminar Room

Hosted by Prof. Maciej Lewenstein