Manifestation of helical edge states as zero-bias magneto-tunneling-conductance peaks in non-centrosymmetric superconductors

Abstract

Helical edge states exist in the mixed spin-singlet and -triplet phase of a noncentrosymmetric superconductor (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 singlet component. We numerically determine energies of these edge states as a function of $γ= Δ_-/Δ_+$. The presence of these edge states is reflected in the tunneling process from a normal metal to an NCSS across a bias energy $eV$: (i) Angle resolved spin conductance (SC) obeying the symmetry $g_s(ϕ) =-g_s(-ϕ)$ shows peaks when the bias energy equals the available quasiparticle edge state energy provided $|eV| \lesssim Δ_-$. (ii) The total SC, $G_s$, is zero but modulates with $eV$ for finite magnetic field $H$. (iii) The zero bias peaks of $G_s$ and total charge conductance, $G_c$, at finite $H$ split into two at finite $eV$ for moderate $H$. (iv) At zero bias, $G_c$ and $G_s$ increase with $H$ and show peaks at $|H|\sim γH_0$ where $H_0$ is a characteristic field.