Electrons on rotationally symmetric nanoparticles under a strong magnetic field

TL;DR

This paper analyzes the energy spectrum of electrons confined to rotationally symmetric nanoparticles under strong magnetic fields, revealing Landau-level-like structures and discussing spectral statistics through analytical and numerical methods.

Contribution

It introduces a method to study electron spectra on surfaces of revolution in magnetic fields, including detailed analysis of spheroids and high-field regimes.

Findings

Energy spectrum exhibits Landau-level-like regularity at high magnetic fields.

Spectral statistics are characterized and discussed.

Analytical and numerical approaches are combined for comprehensive analysis.

Abstract

The energy spectrum of an electron confined to an arbitrary surface of revolution in an external magnetic field, parallel to the symmetry axis, is studied analitycally and numerically. The problem is reduced via conformal mapping to one on the surface of a sphere. The case of a spheroid is considered in details, and the dependence on parameters is discussed. In the high magnetic field limit a regular structure in the energy spectrum, resembling the Landau levels, is obtained. Level statistics is discussed.