Effects of curvature on the electronic states of a two-dimensional mesoscopic ring

TL;DR

This paper investigates how surface curvature influences the electronic states in a two-dimensional mesoscopic ring on a cone, revealing curvature-induced energy shifts and changes in the conducting region, with potential control via magnetic fields.

Contribution

It introduces a detailed analysis of curvature effects on electron states in a mesoscopic ring, highlighting the role of mean curvature and geometric parameters in energy and wave function modifications.

Findings

Curvature decreases energy levels for the $m=0$ state when no magnetic field is present.

The number of occupied states at the Fermi energy is reduced due to curvature effects.

The radial extent of the conducting region is altered by curvature and magnetic control.

Abstract

The effects of surface curvature on the motion of electrons in a mesoscopic two-dimensional ring on a cone in the presence of external magnetic fields are examined. The approach follows the thin-layer quantization procedure, which gives rise to a geometry induced potential. Due to the annular geometric shape of the sample, only the mean curvature has relevant effects to the model. Nevertheless, the most significant contribution of the mean curvature occurs in the state $m=0$, which tends to decrease the energies when the magnetic field is null. The effects of curvature are also manifested in the cyclotron frequency as well as in the effective angular momentum through the $\alpha$ parameter, which can be controlled in such a way that the magnitude of these effects becomes explicit. This is verified in the energies and wave functions of the system. A decrease in the number of occupied states in the Fermi energy is observed. As a consequence, there is an alteration in the radial range of the conducting region of the sample. This fact is confirmed by studying the variations in the radii of the states.