Observation of Quantum Correlations in Topological Solid-state Setups

Abstract

Topological insulators are electronic materials that behave like an ordinary insulator internally (in the bulk), but have symmetry protected conducting states on the edge-sites or surface. The simplest case of non trivial topology found amongst these materials is the one-dimensional Su-Schreifer-Heeger (SSH) model. We analyse the unique features within the non-interacting SSH model and explicitly define both the edge states and the bound states and give the conditions of their presence. We show that the total number of bound states crucially depend on the scattering amplitudes and their phases. The sliding Luttinger liquid (SLL) phase can be destroyed by perturbations such as chargedensity wave (CDW) and superconducting (SC). We construct an analogue of the SSH model by coupling one-dimensional quantum wires packed in a two-dimensional array, with alternating couplings between wires. We calculate the scaling dimensions of the two most relevant (dangerous) perturbations, CDW and SC interwire couplings. We create a phase diagram and analyse whether nearest-neighbour interactions stabilise or destroy the SLL phase. Finally, we find a stability region for the SLL.