Topological mirror insulators in one dimension

We demonstrate the existence of topological insulators in one dimension (1D) protected by mirror and time-reversal symmetries. They are characterized by a nontrivial Z₂ topological invariant defined in terms of the ``partial'' polarizations, which we show to be quantized in the 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 nontrivial state effectively constitute a double-quantum dot with spin-orbit coupling.