Mass-like gap creation by mixed singlet and triplet state in superconducting topological insulator

We investigate proximity-induced mixed spin-singlet and spin-triplet superconducting state on the surface states of a topological insulator. Such hybrid structure features fundamentally distinct electron-hole excitations and resulting effective superconducting subgap. Studying the particle-hole and time-reversal symmetry properties of the mixed state Dirac-Bogoliubov-de Gennes effective Hamiltonian gives rise to manifesting possible topological phase exchange of surface states, since the mixed-spin channels leads to appearance of a band gap on the surface states. This is verified by determining topological invariant winding number for chiral eigenstates, which is achieved by introducing a chiral symmetry operator. We interestingly find the role of mixed superconducting state as creating a mass-like gap in topological insulator by means of introducing new mixed-spin channels $\Delta_1$ and $\Delta_2$. The interplay between superconducting spin-singlet and triplet correlations actually results in gaped surface states, where the size of gap can be controlled by tuning the relative $s$ and $p$-waves pairing potentials. We show that the system is in different topology classes by means of chiral and no-chiral spin-triplet symmetry. In addition, the resulting effective superconductor subgap manipulated at the Fermi surface presents a complicated dependency on mixed-spin channels. Furthermore, we investigate the resulting subgap tunneling conductance in N/S and Josephson current in S/I/S junctions to unveil the influence of effective symmetry of mixed superconducting gap. The results can pave the way to realize the effective superconducting gap in noncentrosymmetric superconductors with mixed-spin state.