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Effective low-energy theory for superconducting topological insulators

Candidate pairings of superconducting topological insulators support interesting surface Andreev bound states (SABSs) known as Majorana fermions. As these materials are described by a two-orbital Bernevig–Hughes–Zhang type model, a general understanding of the low-energy physics such as the possible kinds of SABSs are difficult. By virtue of an analogy between a topological insulator and a time reversal invariant topological superconductor, we propose a simple and intuitive method of constructing the low-energy effective models for superconducting topological insulators like CuxBi2Se3. Depending on the value of the chemical potential and for experimentally relevant model parameters, the low-energy properties of these superconductors are shown to be determined by one copy or two copies of single-orbital effective models. If the effective pairing potential shows sign reversal upon reflection by the surface, one Kramers' pair or two Kramers' pairs of SABSs are expected to appear. Explicit analytical calculations in terms of the effective low energy model reproduce the dispersions of the numerically confirmed two pairs of SABSs for a commonly studied pairing.