Surface Spectral Function of Momentum-dependent Pairing Potentials in a Topological Insulator: Application to Cu$_x$Bi$_2$Se$_3$

We propose three possible momentum-dependent pairing potentials for candidate of topological superconductor (for example Cu$_x$Bi$_2$Se$_3$), and calculate the surface spectral function and surface density of state with these pairing potentials. We find that the first two can give the same spectral functions as the fully-gapped and node-contacted pairing potentials given in [Phys. Rev. Lett. 105, 097001], and that the third one can obtain topological non-trivial case which exists flat Andreev bound state and preserves the $C_3$ rotation symmetry. We hope our proposals and results be judged by future experiment.