Dynamical preparation of Floquet Chern insulators

TL;DR

This paper investigates the dynamics of Floquet topological insulators, showing that while the Chern number remains conserved in infinite systems, boundary effects allow the topological invariant to change, enabling experimental preparation of topological states.

Contribution

It provides an exact analysis of the time evolution in Floquet systems, demonstrating how topological invariants can change in finite systems with boundaries, and explores control of edge current chirality.

Findings

Chern number is conserved in infinite systems under unitary evolution.

The Bott index can change in systems with boundaries, indicating topological transitions.

Edge current chirality can be controlled by adjusting the filling.

Abstract

Realizing topological insulators is of great current interest because of their remarkable properties and possible future applications. There are recent proposals, based on Floquet analyses, that one can generate topologically nontrivial insulators by periodically driving topologically trivial ones. Here we address what happens if one follows the dynamics in such systems. Specifically, we present an exact study of the time evolution of a graphene-like system subjected to a circularly polarized electric field. We prove that, for infinite (translationally invariant) systems, the Chern number is conserved under unitary evolution. For systems with boundaries, on the other hand, we show that a properly defined topological invariant, the Bott index, can change. Hence, it should be possible to experimentally prepare topological states starting from non-topological ones. We show that the chirality of the edge current in such systems can be controlled by adjusting the filling.