Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials

TL;DR

This paper investigates superconducting instabilities on the surface of topological insulators and in noncentrosymmetric materials, revealing regimes with Majorana bound states and contrasting behaviors based on the Fermi level and pairing symmetries.

Contribution

It identifies distinct superconducting regimes and explicitly constructs Majorana bound states in topological surface states and noncentrosymmetric materials, highlighting differences in Majorana fermion numbers.

Findings

Single Majorana fermion in Rashba-Dirac limit vortex

Even number of Majorana fermions in Fermi limit

Superconducting order parameter has mixed s-wave and p-wave components

Abstract

We study the superconducting instabilities of a single species of two-dimensional Rashba-Dirac fermions, as it pertains to the surface of a three-dimensional time-reversal symmetric topological band insulators. We also discuss the similarities as well as the differences between this problem and that of superconductivity in two-dimensional time-reversal symmetric noncentrosymmetric materials with spin-orbit interactions. The superconducting order parameter has both s-wave and p-wave components, even when the superconducting pair potential only transfers either pure singlets or pure triplets pairs of electrons in and out of the condensate, a corollary to the non-conservation of spin due to the spin-orbit coupling. We identify one single superconducting regime in the case of superconductivity in the topological surface states (Rashba-Dirac limit), irrespective of the relative strength between singlet and triplet pair potentials. In contrast, in the Fermi limit relevant to the noncentrosymmetric materials we find two regimes depending on the value of the chemical potential and the relative strength between singlet and triplet potentials. We construct explicitly the Majorana bound states in these regimes. In the single regime for the case of the Rashba-Dirac limit, there exist one and only one Majorana fermion bound to the core of an isolated vortex. In the Fermi limit, there are always an even number (0 or 2 depending on the regime) of Majorana fermions bound to the core of an isolated vortex. In all cases, the vorticity required to bind Majorana fermions is unity, in contrast to the half-flux in the case of two-dimensional $p_x \pm i p_y$ superconductors that break time-reversal symmetry.