Electron states in a two-dimensional ring - an exactly soluble model

Abstract

An exactly soluble model for a two-dimensional ring is proposed. Using this model, we have obtained analytically the energy spectrum and wavefunctions for a ring in the presence of a uniform magnetic field and a thin magnetic flux. The model can also describe quantum dots, anti-dots, one-dimensional rings and straight two-dimensional wires, which provides an integrated picture for the electron states and their magnetic field response in these geometries. The simplicity and the flexibility of the model make it an ideal tool for the modelling of the Aharonov-Bohm effects and the persistent currents in quantum rings.

Quasistates and their relation to the Dicke effect in a mesoscopic ring coupled to a reservoir

“…(1). In the single particle picture a ring of finite width can be solved analytically 22,23 . We have used the one-dimensional energy spectrum to keep the calculations tractable, which is a good approximation for thin rings.…”

A comment on the analogous confinement of a neutral particle to a quantum dot via noninertial effects

“…[33][34][35][36][37]. Further, by assuming that the parameter δ = E 0 ω is small, we have shown that the spectrum of energy is proportional to 2 in contrast to previous studies of the analogous confinement of a neutral particle with a permanent magnetic dipole moment to a quantum dot induced by noninertial effects [30,31], where the energy levels are proportional to in an analogous way to the Tan-Inkson model for a quantum dot [53][54][55]. Moreover, we have also obtained the Page-Werner et al term [11][12][13], which corresponds to the coupling between the quantum number and the angular velocity ω.…”

“…Comparing the result (12) with the studies of the confinement of particles to a quantum dot made in [33][34][35][36][37], we have in this case that the geometry of the spacetime plays the role of a hard-wall confining potential due to the presence of noninertial effects that restrict the physical region of the spacetime where the wave function can be defined. Moreover, we have that the energy levels (12) are proportional to 2 in contrast to recent studies of the analogous confinement of a neutral particle to a quantum dot [30,31] (given by imposing a condition on the induced fields µλ ω), where the energy levels are proportional to in an analogous way to the Tan-Inkson model for a quantum dot [53][54][55]. Hence, the spectrum of energy (12) is analogous to having a neutral particle with a permanent electric dipole moment confined to a quantum dot described by a hard-wall confining potential [33][34][35][36][37].…”

“…A similar analysis has been made in [30][31][32] to achieve discrete energy levels of a neutral particle with permanent magnetic dipole moment confined to a parabolic potential analogous to the Tan-Inkson potential for a quantum dot [53][54][55], and in [21] to achieve the Landau-Aharonov-Casher quantization in a rotating frame. Here, we bring the discussion of obtaining bounds states for a neutral particle in the present noninertial system without imposing the above condition on the induced fields.…”

On noninertial effects inducing a confinement of a neutral particle to a hard-wall confining potential

“…In recent years, the study of the confinement of particles in two-dimensional quantum rings and quantum dots have been made in different models [32][33][34][36][37][38][39][40][41][42][43][44]. An interesting discussion about the behaviour of a quantum particle confined to a quantum two-dimensional quantum ring and a quantum dot was made in [32][33][34][40][41][42][43], where it has been shown that the spectrum of energy can be either non-parabolic [40][41][42] or parabolic [32][33][34]43] in relation to the principal quantum number…”