Topological Mirror Insulators in One Dimension

TL;DR

This paper establishes the existence of one-dimensional topological insulators protected by mirror and time-reversal symmetries, characterized by a quantized $\

Contribution

It introduces a new $\

Findings

Presence of boundary charges at mirror-symmetric boundaries

Existence of in-gap end-mode Kramers doublets in non-trivial states

Topological invariant defined via partial polarizations

Abstract

We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the "partial" polarizations, which we show to be quantized in presence of a 1D mirror point. The topological invariant determines the generic presence or absence of integer boundary charges at the mirror-symmetric boundaries of the system. We check our findings against spin-orbit coupled Aubry-Andr\'e-Harper models that can be realized, e.g. in cold-atomic Fermi gases loaded in one-dimensional optical lattices or in density- and Rashba spin-orbit-modulated semiconductor nanowires. In this setup, in-gap end-mode Kramers doublets appearing in the topologically non-trivial state effectively constitute a double-quantum-dot with spin-orbit coupling.