Suppression of the overlap between Majorana fermions by orbital magnetic effects in semiconducting-superconducting nanowires

TL;DR

This paper investigates how orbital magnetic effects influence Majorana fermions in semiconducting nanowires, revealing that these effects can suppress oscillations in energy splitting, contrasting with previous models neglecting orbital contributions.

Contribution

The study introduces a simplified model incorporating orbital effects as a chemical potential shift, providing new insights into Majorana fermion behavior under magnetic fields.

Findings

Orbital effects can be modeled as a chemical potential shift.

Orbital effects can suppress or alter Majorana energy splitting oscillations.

Oscillation periods remain nearly constant in many regimes.

Abstract

We study both analytically and numerically the role of orbital effects caused by a magnetic field applied along the axis of a semiconducting Rashba nanowire in the topological regime hosting Majorana fermions. We demonstrate that the orbital effects can be effectively taken into account in a one-dimensional model by shifting the chemical potential, and, thus modifying the topological criterion. We focus on the energy splitting between two Majorana fermions in a finite nanowire and find a striking interplay between orbital and Zeeman effects on this splitting. In the limit of strong spin-orbit interaction, we find regimes where the amplitude of the oscillating splitting stays constant or even decays with increasing magnetic field, in stark contrast to the commonly studied case where orbital effects of the magnetic field are neglected. The period of these oscillations is found to be almost constant in many parameter regimes.