Instability of topological order and localization of edge states in HgTe quantum wells coupled to s-wave superconductor

Using microscopic tight-binding equations we derive the effective Hamiltonian for a two-layer hybrid structure comprising a two-dimensional HgTe quantum-well-based topological insulator (TI) coupled to an s-wave isotropic superconductor and show that it contains terms describing the mixing of TI subband branches by superconducting correlations induced by the proximity effect. We find that the proximity effect breaks down the rotational symmetry of the TI spectrum. We show that the edge states not only acquire a gap, as follows from the standard theory, but can also become localized by the Andreev-backscattering mechanism in a small coupling regime. In a strong-coupling regime the edge states merge with the bulk states, and the TI transforms into an anisotropic narrow-gap semiconductor.