Orbital effect of magnetic field on the Majorana phase diagram

TL;DR

This paper investigates how the orbital effect of magnetic fields influences Majorana states in semiconducting nanowires, revealing significant impacts on the phase diagram, band gap, and symmetry considerations crucial for experimental design.

Contribution

It systematically analyzes the orbital magnetic field effect on Majorana nanowires, highlighting its dominance over Zeeman effects and implications for topological phase stability.

Findings

Orbital magnetic field effect surpasses Zeeman effect in impact.

Multiple subband filling leads to impractically large Majoranas and small band gaps.

Magnetic field alignment with the wire preserves the topological gap due to symmetry.

Abstract

Studies of Majorana bound states in semiconducting nanowires frequently neglect the orbital effect of magnetic field. Systematically studying its role leads us to several conclusions for designing Majoranas in this system. Specifically, we show that for experimentally relevant parameter values orbital effect of magnetic field has a stronger impact on the dispersion relation than the Zeeman effect. While Majoranas do not require a presence of only one dispersion subband, we observe that the size of the Majoranas becomes unpractically large, and the band gap unpractically small when more than one subband is filled. Since the orbital effect of magnetic field breaks several symmetries of the Hamiltonian, it leads to the appearance of large regions in parameter space with no band gap whenever the magnetic field is not aligned with the wire axis. The reflection symmetry of the Hamiltonian with respect to the plane perpendicular to the wire axis guarantees that the wire stays gapped in the topologically nontrivial region as long as the field is aligned with the wire.