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We present microscopic, self-consistent calculations of the superconducting order parameter and pairing correlations near the interface of an $s$-wave superconductor and a three-dimensional topological insulator with spin-orbit coupling. We discuss the suppression of the order parameter by the topological insulator and show that the equal-time pair correlation functions in the triplet channel, induced by spin-flip scattering at the interface, are of $p_xpm i p_y$ symmetry. We verify that the spectrum at sub-gap energies is well described by the Fu-Kane model. The sub-gap modes are viewed as interface states with spectral weight penetrating well into the superconductor. We extract the phenomenological parameters of the Fu-Kane model from microscopic calculations, and find they are strongly renormalized from the bulk material parameters. This is consistent with previous results of Stanescu et al for a lattice model using perturbation theory in the tunneling limit.
Realization of topological superconductors (TSCs) hosting Majorana fermions is a central challenge in condensed-matter physics. One approach is to use the superconducting proximity effect (SPE) in heterostructures, where a topological insulator conta
We study the proximity effect between the fully-gapped region of a topological insulator in direct contact with an s-wave superconducting electrode (STI) and the surrounding topological insulator flake (TI) in Au/Bi$_{1.5}$Sb$_{0.5}$Te$_{1.7}$Se$_{1.
The combination of superconductivity and the helical spin-momentum locking at the surface state of a topological insulator (TI) has been predicted to give rise to p-wave superconductivity and Majorana bound states. The superconductivity can be induce
Superconducting topological crystalline insulators (TCI) are predicted to host new topological phases protected by crystalline symmetries, but available materials are insufficiently suitable for surface studies. To induce superconductivity at the sur
The proximity coupled topological insulator / superconductor (TI/SC) bilayer system is a representative system to realize topological superconductivity. In order to better understand this unique state and design devices from the TI/SC bilayer, a comp