Manifestation of helical edge states as zero bias magneto-tunneling-conductance peaks innoncentrosymmetric superconductors

Abstract

Helical edge states exist in the mixed spin singlet and triplet phase of a noncentrosymmetricsuperconductor (NCSS) when the pair amplitude (PA) in the negative helicity band,Δ−, is smaller than the PA in the positive helicity band,Δ+, i.e., when the PA in the triplet component is more than the same in the singletcomponent. We numerically determine energies of these edge states as a function ofγ = Δ−/Δ+. The presence of these edge states is reflected in the tunnelingprocess from a normal metal to an NCSS across a bias energyeV. (i) Angle resolved spin conductance (SC) obeying the symmetrygs(ϕ) = −gs(−ϕ) shows peaks when the bias energy equals the available quasiparticle edge state energyprovided . (ii) The total SC, Gs, iszero but modulates with eV for finite magnetic field H.(iii) The zero bias peaks of Gs and total charge conductance, Gc, at finite H splitinto two at finite eV for moderate H.(iv) At zero bias, Gc and Gs increasewith H andshow peaks at |H|∼γH0, where H0 is a characteristic field.