Nature of the zero-bias conductance peak associated with Majorana bound states in topological phases of semiconductor-superconductor hybrid structures

TL;DR

This paper investigates the zero-bias conductance peak in semiconductor-superconductor hybrid structures supporting Majorana bound states, explaining discrepancies between experimental observations and theoretical predictions through detailed non-equilibrium transport modeling.

Contribution

It introduces a microscopic, non-equilibrium Green's function approach to model tunneling and conductance, revealing how tunnel coupling and magnetic fields influence the ZBCP.

Findings

ZBCP height depends on tunnel coupling and can be less than 2e^2/h.

Splitting of ZBCP occurs with increasing magnetic field beyond critical value.

Behavior of ZBCP varies with gate-controlled potential and across topological phase transition.

Abstract

Rashba spin-orbit coupled semiconductor-superconductor hybrid structures in the presence of Zeeman splitting have emerged as the first experimentally realizable topological superconductor supporting zero-energy Majorana bound states. However, recent experimental studies in these hybrid structures are not in complete agreement with the theoretical predictions, for example, the observed height of the zero-bias conductance peak (ZBCP) associated with the Majorana bound states is less than 10% of the predicted quantized value 2e^2/h. We try to understand the sources of various discrepancies between the recent experiments and the earlier theories by starting from a microscopic theory and studying non-equilibrium transport in these systems at arbitrary temperatures and applied bias voltages. Our approach involves quantum Langevin equations and non-equilibrium Green's functions. Here we are able to model the tunnel coupling between the one-dimensional semiconductor-superconductor hybrid structure and the metallic leads realistically; study the role of tunnel coupling on the height of the ZBCP and the subgap conductance; predict the nature of the splitting of the ZBCP with an increasing magnetic field beyond the critical field; show the behavior of the ZBCP with an increasing gate-controlled onsite potential; and study the evolution of the full differential conductance across the topological quantum phase transition. When the applied magnetic field is quite large compared to the Rashba splitting and the bulk energy gap is much reduced, we find the ZBCP even for an onsite potential much larger than the applied magnetic field. The height of the corresponding ZBCP depends on the tunnel coupling even at zero temperature and can be much smaller than 2e^2/h.