A Superconducting instability in the surface of a topological insulator

It is argued that a superconducting instability appears in the electronic states on the surface of a topological insulator due purely to electromagnetic interactions. The discussion of this instability is based on the analysis of the effective Coulomb interaction and the assumption that the system behaves like a two dimensional Fermi liquid. It is shown that this superconducting instability appears in the p-wave channel (like in the pure QED$_{3}$ case) and an expression for the critical temperature of the transition is provided.