Phase diagrams of superconducting topological surface states

In this paper, we present a detailed study on the phase diagrams of superconducting topological surface states, especially, focusing on the interplay between crystalline symmetry and topology of the effective BdG Hamiltonian. We show that for the $4\times 4$ kinematic Hamiltonian of the normal state, a mirror symmetry $\mathcal{M}$ can be defined, and for the $\mathcal{M}$-odd pairings, the classification of the $8\times8$ BdG Hamiltonian is $\mathbb{Z}\oplus\mathbb{Z}$, and the time-reversal symmetry is broken intrinsically. The topological non-trivial phase can support chiral Majorana edge modes, and can be realized in the thin films of iron-based superconductor such as FeSeTe.