Effects of Curvature on the Electronic States of a Two-Dimensional Mesoscopic Ring

We study the effects of curvature on an electron in a two-dimensional localized annular region in the presence of external magnetic fields. The approach follows the thin-layer quantization procedure. We verify that the most significant contribution of the mean curvature occurs in the state with m=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m=0$$\end{document}, which tends to decrease the energies in null magnetic fields. The effects of curvature are also manifested in the cyclotron frequency as well as in the effective angular momentum through the α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} 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, which leads to an alteration in the radial range of the conducting region of the sample. This is confirmed by studying the variations in the radii of the states.