Nematic superconductivity in CuxBi2Se3 : Surface Andreev bound states

We study theoretically the topological surface states (TSSs) and the possible surface Andreev bound states (SABSs) of ${\mathrm{Cu}}_x{\mathrm{Bi}}₂{\mathrm{Se}}₃$, which is known to be a topological insulator at $x=0$. The superconductivity (SC) pairing of this compound is assumed to have broken spin-rotation symmetry, similar to that of the A-phase of $³\mathrm{He}$ as suggested by recent nuclear-magnetic resonance experiments. For both spheroidal and corrugated cylindrical Fermi surfaces with the hexagonal warping terms, we show that the bulk SC gap is rather anisotropic; the minimum of the gap is negligibly small as compared to the maximum of the gap. This would make the fully gapped pairing effectively nodal. For a clean system, our results indicate the bulk of this compound to be a topological superconductor with the SABSs appearing inside the bulk SC gap. The zero-energy SABSs, which are Majorana fermions, together with the TSSs not gapped by the pairing, produce a zero-energy peak in the surface density of states (SDOS). The SABSs are expected to be stable against short-range nonmagnetic impurities, and the local SDOS is calculated around a nonmagnetic impurity. The relevance of our results to experiments is discussed.