Nematic superconductivity in Cu$_{x}$Bi$_{2}$Se$_{3}$: The surface Andreev bound states

TL;DR

This paper theoretically investigates the topological surface states and surface Andreev bound states in Cu$_{x}$Bi$_{2}$Se$_{3}$, revealing anisotropic gaps, potential Majorana fermions, and implications for experimental detection of topological superconductivity.

Contribution

It provides a theoretical analysis of surface states and Andreev bound states in Cu$_{x}$Bi$_{2}$Se$_{3}$, highlighting the potential for Majorana fermions and topological superconductivity.

Findings

Bulk superconducting gap is anisotropic and effectively nodal.

Zero-energy Majorana bound states appear inside the superconducting gap.

Surface density of states shows a zero-energy peak due to Majorana 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.