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

TL;DR

This paper investigates how periodic electric fields can create and control localized edge states in one-dimensional tight-binding models, including non-interacting and interacting bosonic systems, using Floquet theory.

Contribution

It demonstrates the generation of edge states through Floquet engineering in both non-interacting and interacting systems, with a theoretical framework for understanding these effects.

Findings

Periodic driving induces localized edge states in non-interacting models.

Edge states can be generated in interacting bosonic systems with Hubbard interactions.

Edge states are detectable via differential conductance measurements.

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.