Snaking states on a cylindrical surface in a perpendicular magnetic field

TL;DR

This paper models electronic states on a cylindrical nanowire surface in a perpendicular magnetic field, revealing localized cyclotron and snaking orbits, and explores the effects of spin-orbit interactions on charge density distribution.

Contribution

It introduces a detailed analysis of electron localization and orbital behavior on a cylindrical surface under magnetic fields, including spin-orbit effects, for finite and infinite nanowires.

Findings

Cyclotron states localize at North and South poles with increasing magnetic field.

Snaking states propagate along the East-West sides, stable in energy.

Spin-orbit interactions cause axial twisting of charge density in finite-length cylinders.

Abstract

We calculate electronic states on a closed cylindrical surface as a model of a core-shell nanowire. The length of the cylinder can be infinite or finite. We define cardinal points on the circumference of the cylinder and consider a spatially uniform magnetic field perpendicular to the cylinder axis,in the direction South-North. The orbital motion of the electrons depends on the radial component of the field which is not uniform around the circumference: it is equal to the total field at North and South, but vanishes at the West and East sides. For a strong field, when the magnetic length is comparable to the radius of the cylinder, the electronic states at North and South become localized cyclotron orbits, whereas at East and West the states become long and narrow snaking orbits propagating along the cylinder. The energy of the cyclotron states increases with the magnetic field whereas the energy of the snaking states is stable. Consequently, at high magnetic fields the electron density vanishes at North and South and concentrates at East and West. We include spin-orbit interaction with linear Rashba and Dresselhaus models. For a cylinder of finite length the Dresselhaus interaction produces an axial twist of the charge density relative to the center of the wire, which may be amplified in the presence of the Rashba interaction.