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Abstract: We study the superconducting instabilities of a single species oftwo-dimensional Rashba-Dirac fermions, as it pertains to the surface of athree-dimensional time-reversal symmetric topological band insulators. We alsodiscuss the similarities as well as the differences between this problem andthat of superconductivity in two-dimensional time-reversal symmetricnoncentrosymmetric materials with spin-orbit interactions. The superconductingorder parameter has both s-wave and p-wave components, even when thesuperconducting pair potential only transfers either pure singlets or puretriplets pairs of electrons in and out of the condensate, a corollary to thenon-conservation of spin due to the spin-orbit coupling. We identify one singlesuperconducting regime in the case of superconductivity in the topologicalsurface states Rashba-Dirac limit, irrespective of the relative strengthbetween singlet and triplet pair potentials. In contrast, in the Fermi limitrelevant to the noncentrosymmetric materials we find two regimes depending onthe value of the chemical potential and the relative strength between singletand triplet potentials. We construct explicitly the Majorana bound states inthese 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 isolatedvortex. In the Fermi limit, there are always an even number 0 or 2 dependingon the regime of Majorana fermions bound to the core of an isolated vortex. Inall cases, the vorticity required to bind Majorana fermions is unity, incontrast to the half-flux in the case of two-dimensional $p x \pm i p y$superconductors that break time-reversal symmetry.



Author: Luiz Santos, Titus Neupert, Claudio Chamon, Christopher Mudry

Source: https://arxiv.org/







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