Floquet engineering of edge states in the presence of staggered potential and interactions

Abstract

We study the effects of a periodically driven electric field applied to a variety of tight-binding models in one dimension. We first consider a non-interacting system with or without a staggered on-site potential, and we find that that periodic driving can generate states localized completely or partially near the ends of a finite-sized system. Depending on the system parameters, such states have Floquet eigenvalues lying either outside or inside the continuum of eigenvalues of the bulk states; only in the former case we find that these states are completely localized at the ends and are true edge states. We then consider a system of two bosonic particles which have an on-site Hubbard interaction and show that a periodically driven electric field can generate two-particle states which are localized at the ends of the system. We show that many of these effects can be understood using a Floquet perturbation theory which is valid in the limit of large staggered potential or large interaction strength. Some of these effects can also be understood qualitatively by considering time-independent Hamiltonians which have a potential at the sites at the edges; Hamiltonians of these kind effectively appear in a Floquet-Magnus analysis of the driven problem. Finally, we discuss how the edge states produced by periodic driving of a non-interacting system of fermions can be detected by measuring the differential conductance of the system.

25 pages, 23 figures; made some significant changes in the text and figures, added some references

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Cited by in corpus (3)

• Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols