Two-dimensional electron gas under the effect of constrained potential and magnetic field in curved space

TL;DR

This paper investigates how the curvature of a cylindrical surface influences the energy spectrum of a two-dimensional electron gas in a magnetic field, providing perturbative corrections and comparing curved and flat geometries.

Contribution

It introduces the first perturbative analytical corrections to the energy spectrum of a curved 2D electron gas in a magnetic field, advancing beyond previous numerical approaches.

Findings

Derived perturbative corrections to energy spectrum due to curvature

Compared energy spectra of curved and flat surfaces

Showed curvature effects modify the dispersion relationship

Abstract

The effect of the curvature of a cylindrical surface on the energy spectrum for a curved two-dimensional electron gas in a homogeneous magnetic field is considered. The corrections to the energy spectrum are obtained for the first time perturbatively, in contrast to previous works where it was obtained numerically. The dispersion relationship is obtained as a function of curvature radius and the results for curved surface have been compared with the flat surface.