Conductance spectroscopy of nontopological-topological superconductor junctions

TL;DR

This paper calculates the differential conductance of a junction between nontopological and topological superconductors, revealing how conductance features depend on junction transparency and can mimic Majorana signatures.

Contribution

It provides a comprehensive analysis of conductance spectra in superconductor junctions, including effects of transparency and the potential for false-positive Majorana signatures.

Findings

Quantized conductance peaks at $eV=\pm \Delta_s$ in tunneling limit

Finite subgap conductance due to multiple Andreev reflections at higher transparency

Zero-energy states can mimic Majorana conductance signatures

Abstract

We calculate the zero-temperature differential conductance $dI/dV$ of a voltage-biased one-dimensional junction between a nontopological and a topological superconductor for arbitrary junction transparency using the scattering matrix formalism. We consider two representative models for the topological superconductors: (i) spinful $p$-wave and (ii) $s$-wave with spin-orbit coupling and spin splitting. We verify that in the tunneling limit (small junction transparencies) where only single Andreev reflections contribute to the current, the conductance for voltages below the nontopological superconductor gap $\Delta_s$ is zero and there are two symmetric conductance peaks appearing at $eV = \pm \Delta_s$ with the quantized value $(4-\pi)2e^2/h$ due to resonant Andreev reflection from the Majorana zero mode. However, when the junction transparency is not small, there is a finite conductance for $e|V| < \Delta_s$ arising from multiple Andreev reflections. The conductance at $eV = \pm \Delta_s$ in this case is no longer quantized. In general, the conductance is particle-hole asymmetric except for sufficiently small transparencies. We further show that, for certain values of parameters, the tunneling conductance from a zero-energy conventional Andreev bound state can be made to mimic the conductance from a true Majorana mode.