Wave functions for a toroidal quantum dot in the presence of an axially symmetric magnetic field: transition from ring to bulk states as a function of aspect ratio

Abstract

A basis set expansion is employed to calculate spectra and eigenstates of charge carriers within a toroidal volume characterized by major radius $R$ and minor radius $a$ immersed in an azimuthally symmetric magnetic field. The angular variables appearing in the Schrodinger equation are eliminated by contour methods, yielding effective potentials that reduce computational time by a large factor. An approximation formula for the single particle spectrum is presented that allows efficient construction of the partition function necessary for rapid calculation of thermodynamic quantities. The heat capacity from as a function of torus aspect ratio and temperature is calculated. The transition from ring-type to bulk-type behavior of the heat capacity is presented.