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We investigate proximity-induced mixed spin-singlet and spin-tripletsuperconducting state on the surface states of a topological insulator. Suchhybrid structure features fundamentally distinct electron-hole excitations andresulting effective superconducting subgap. Studying the particle-hole andtime-reversal symmetry properties of the mixed state Dirac-Bogoliubov-de Genneseffective Hamiltonian gives rise to manifesting possible topological phaseexchange of surface states, since the mixed-spin channels leads to appearanceof a band gap on the surface states. This is verified by determiningtopological invariant winding number for chiral eigenstates, which is achievedby introducing a chiral symmetry operator. We interestingly find the role ofmixed superconducting state as creating a mass-like gap in topologicalinsulator by means of introducing new mixed-spin channels $\Delta_1$ and$\Delta_2$. The interplay between superconducting spin-singlet and tripletcorrelations actually results in gaped surface states, where the size of gapcan 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 andno-chiral spin-triplet symmetry. In addition, the resulting effectivesuperconductor subgap manipulated at the Fermi surface presents a complicateddependency on mixed-spin channels. Furthermore, we investigate the resultingsubgap tunneling conductance in N/S and Josephson current in S/I/S junctions tounveil the influence of effective symmetry of mixed superconducting gap. Theresults can pave the way to realize the effective superconducting gap innoncentrosymmetric superconductors with mixed-spin state.

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