For systems that can be modeled as a single-particle lattice extended along aprivileged direction as, e.g., quantum wires, the so-called eigenvalue methodprovides full information about the propagating and evanescent modes as afunction of energy. This complex-band structure method can be applied either tolattices consisting of an infinite succession of interconnected layersdescribed by the same local Hamiltonian or to superlattices: Systems in whichthe spatial periodicity involves more than one layer. Here, for time-dependentsystems subject to a periodic driving, we present an adapted version of thesuperlattice scheme capable of obtaining the Floquet states and the Floquetquasienergy spectrum. Within this scheme the time periodicity is treated asexisting along spatial dimension added to the original system. The solutions ata single energy for the enlarged artificial system provide the solutions of theoriginal Floquet problem. The method is suited for arbitrary periodicexcitations including strong and anharmonic drivings. We illustrate thecapabilities of the methods for both time-independent and time-dependentsystems by discussing: (a) topological superconductors in multimode quantumwires with spin-orbit interaction and (b) microwave driven quantum dot incontact with a topological superconductor.
展开▼
