# Tunneling conductance in semiconductor-superconductor hybrid structures

## TL;DR

This paper investigates how tunneling conductance in semiconductor-superconductor hybrid structures reveals the effects of disorder, magnetic fields, and coupling strength on Majorana zero modes, highlighting challenges in realizing topological quantum states.

## Contribution

It introduces a comprehensive model treating the superconductor as an active component, showing how sub-gap states affect conductance features and the stability of Majorana modes.

## Key findings

- Sub-gap states cause particle-hole asymmetry in conductance.
- Disorder and magnetic fields lead to breakdown of zero-bias peak quantization.
- Coupling strength influences the low-energy conductance behavior.

## Abstract

We study the differential conductance for charge tunneling into a semiconductor wire--superconductor hybrid structure, which is actively investigated as a possible scheme for realizing topological superconductivity and Majorana zero modes. The calculations are done based on a tight-binding model of the heterostructure using both a Blonder-Tinkham-Klapwijk approach and a Keldysh non-equilibrium Green's function method. The dependence of various tunneling conductance features on the coupling strength between the semiconductor and the superconductor, the tunnel barrier height, and temperature is systematically investigated. We find that treating the parent superconductor as an active component of the system, rather than a passive source of Cooper pairs, has qualitative consequences regarding the low-energy behavior of the differential conductance. In particular, the presence of sub-gap states in the parent superconductor, due to disorder and finite magnetic fields, leads to characteristic particle-hole asymmetric features and to the breakdown of the quantization of the zero-bias peak associated with the presence of Majorana zero modes localized at the ends of the wire. The implications of these findings for the effort toward the realization of Majorana bound states with true non-Abelian properties are discussed.