Curvature of gap closing features and the extraction of Majorana nanowire parameters

TL;DR

This paper analyzes how the curvature of the superconducting gap closing in Majorana nanowires, influenced by magnetic field, reveals key microscopic parameters like spin-orbit coupling and g-factor, aiding in better modeling of these systems.

Contribution

It introduces a method to extract the effective g-factor and constrain microscopic parameters from the curvature of the gap closing feature in experimental data.

Findings

Concave gap closing indicates strong spin-orbit coupling.

Non-linear gap closing affects g-factor estimation.

Measurement of gap closure provides insights into nanowire parameters.

Abstract

Recent tunneling conductance measurements of Majorana nanowires show a strong variation in the magnetic field dependence of the superconducting gap among different devices. Here, we theoretically study the magnetic field dependence of the gap closing feature and establish that the degree of convexity (or concavity) of the gap closing as a function of Zeeman field can provide critical constraints on the underlying microscopic parameters of the semiconductor-superconductor hybrid system model. Specifically, we show that the gap closing feature is entirely concave only for strong spin-orbit coupling strength relative to the chemical potential. Additionally, the non-linearity (i.e. concavity or convexity) of the gap closing as a function of magnetic field complicates the simple assignment of a constant effective $ g $-factor to the states in the Majorana nanowire. We develop a procedure to estimate the effective $ g $-factor from recent experimental data that accounts for the non-linear gap closing resulting from the interplay between chemical potential and spin-orbit coupling. Thus, measurements of the magnetic field dependence of the gap closure on the trivial side of the topological quantum phase transition can provide useful information on parameters that are critical to the theoretical modeling of Majorana nanowires.