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

TL;DR

This paper investigates helical edge states in noncentrosymmetric superconductors, revealing how they manifest as zero-bias magneto-tunneling conductance peaks and depend on the ratio of pair amplitudes in different helicity bands.

Contribution

It numerically analyzes the energies of helical edge states and their signatures in tunneling conductance, highlighting their dependence on the pair amplitude ratio and magnetic field effects.

Findings

Edge states cause zero-bias conductance peaks in tunneling spectra.

Magneto-tunneling conductance peaks split and modulate with magnetic field.

Conductance peaks are linked to the ratio of pair amplitudes in helicity bands.

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, $\Delta_-$, is smaller than the PA in the positive helicity band, $\Delta_+$, 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 $\gamma = \Delta_-/\Delta_+$. 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 $g_s(\phi) =-g_s(-\phi)$ shows peaks when the bias energy equals the available quasiparticle edge state energy provided $|eV| \lesssim \Delta_-$. (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 $|H|\sim \gamma H_0$ where $H_0$ is a characteristic field.