Superconductivity in the surface states of a Bi2X3 topological insulator: effects of a realistic model

Superconductivity in the topological surface states is essential to both the surface spectrum of bulk superconducting state and the proximity-induced superconductivity of Bi2X3 (X is Se or Te) topological insulators. While previous theories were mostly based on simplified models for the bulk topological insulator and the surface states, the accumulating experiments stimulate us to make an analysis using realistic model for the normal state electronic structures, incorporating terms responsible for particle-hole asymmetry and hexagonal warping. An effective low-energy model for the topological surface states is derived first. Then we identify all the bulk time-reversal-invariant superconducting pairings in the topological insulator that can open a gap in the topological surface states. Many more pairings are found to be able to gap the topological surface states as compared to conclusions based on simplified models. The number of proximity-induced pairing channels in the topological surface states increases by one as a result of the hexagonal warping term, but is not changed by the particle-hole asymmetry term.