Proximity-induced unconventional superconductivity in topological insulators

We study proximity-induced superconducting pairing in a three-dimensional topological insulator - superconductor hybrid structure for superconductors with different pairing symmetries. The Dirac surface state in the topological insulator gives rise to a coupling between spin-singlet and spin-triplet pairing amplitudes as well as pairing that is odd in frequency for $p$-wave superconductors. We also find that all superconductors induce pairing that is odd in both frequency and orbital (band) index, with a complete reciprocity between pairing in orbital index and frequency. We show that the different induced pairing amplitudes significantly modify the density of states in the TI surface layer.