Electronic transport in one-dimensional Floquet topological insulators via topological and nontopological edge states

TL;DR

This paper proposes an experimental method to probe topological and non-topological edge states in one-dimensional Floquet topological insulators using electronic transport measurements, revealing new states related to extremal points in the dispersion.

Contribution

It introduces a transport-based experimental test for the topological phase diagram and uncovers non-topological edge states arising from extremal points in the dispersion relation.

Findings

Transport peaks at topological gap indicate edge states.

Additional peaks at extremal points reveal non-topological edge states.

Non-topological states are linked to Van Hove singularities and are likely present in similar systems.

Abstract

Based on probing electronic transport properties we propose an experimental test for the recently discovered rich topological phase diagram of one-dimensional Floquet topological insulators with Rashba spin-orbit interaction [Kennes \emph{et al.}, Phys. Rev. B {\bf 100}, 041103(R) (2019)]. Using the Keldysh-Floquet formalism we compute electronic transport properties of these nanowires, where we propose to couple the leads in such a way, as to primarily address electronic states with a large weight at one edge of the system. By tuning the Fermi energy of the leads to the center of the topological gap we are able to directly address the topological edge states, granting experimental access to the topological phase diagram. Surprisingly, when tuning the lead Fermi energy to special values in the bulk which coincide with extremal points of the dispersion relation, we find additional peaks of similar magnitude to those caused by the topological edge states. These peaks reveal the presence of continua of states centered around aforementioned extremal points whose wavefunctions are linear combinations of delocalized bulk states and exponentially localized edge states, where the ratio of edge- to bulk-state amplitude is maximal at the extremal point of the dispersion. We discuss the transport properties of these \emph{non-topological edge states}, explain their emergence in terms of an intuitive yet quantitative physical picture and discuss their relationship with Van Hove singularities in the bulk of the system. The mechanism giving rise to these states is not specific to the model we consider here, suggesting that they may be present in a wide class of one-dimensional systems.