Nematic superconductivity in Cu${}_x$Bi${}_2$Se${}_3$: The surface Andreev bound states

Abstract

We study theoretically the topological surface states (TSSs) and the possible surface Andreev bound states (SABSs) of Cu${}_x$Bi${}_2$Se${}_3$ which is known to be a topological insulator at $x=0$. The superconductivity (SC) pairing of this compound is assumed to have the broken spin-rotation symmetry, similar to that of the A-phase of ${}^3$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 comparing 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.

11 pages, 6 figures

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• Possible two-component pairings in electron-doped Bi${}_2$Se${}_3$ based on a tight-binding model
• Anomalous Josephson Hall effect in doped topological insulators with the nematic superconductivity
• On the existence of nematic-superconducting states in the Ginzburg-Landau regime