We study the surface state of a doped topological crystalline insulator in the superconducting state. Motivated by Sn$_{1-x}$In$_x$Te, we consider fully gapped pair potentials and calculate the surface spectral function. It is found that mirror-prote
cted zero-energy Andreev bound states appear at the (001) surface and that these states can move along the mirror symmetric line on the surface Brillouin zone. We also show that the surface Andreev bound state changes systematically with doping due to the presence of the Dirac surface state in the normal state.
We study bulk electronic states of superconducting topological insulator, which is the promising candidate for topological superconductor. Recent experiments suggest that the three-dimensional Fermi surface evolves into two-dimensional one. We show t
hat the superconducting energy gap structure on the Fermi surface systematically changes with this evolution. It is clarified that the bulk electronic properties such as spin-lattice relaxation rate and specific heat depend on the shape of the Fermi surface and the type of the energy gap function. These results serve as a guide to determine the pairing symmetry of Cu$_x$Bi$_2$Se$_3$.
We study electronic properties of a superconducting topological insulator whose parent material is a topological insulator. We calculate the temperature dependence of the specific heat and spin susceptibility for four promising superconducting pairin
gs proposed by L. Fu and E. Berg (Phys. Rev. Lett. 105, 097001). Since the line shapes of temperature dependence of specific heat are almost identical among three of the four pairings, it is difficult to identify them simply from the specific heat. On the other hand, we obtain wide varieties of the temperature dependence of spin susceptibility for each pairing reflecting the spin structure of Cooper pair. We propose that the pairing symmetry of superconducting topological insulator can be determined from measurement of Knight shift by changing the direction of applied magnetic field.
