Electron wave functions on in a static magnetic field of arbitrary direction

Abstract

A basis set expansion is performed to find the eigenvalues and wave functions for an electron on a toroidal surface T 2 subject to a constant magnetic field in an arbitrary direction. The evolution of several low-lying states as a function of field strength and field orientation is reported, and a procedure to extend the results to include two-body Coulomb matrix elements on T 2 is presented.

Coupling curvature to a uniform magnetic field: An analytic and numerical study

“…Here the latter approach will be adopted in order to facilitate comparisons to a related work [6] and because of the ease by which the Hamiltonian matrix elements…”

“…Nanostructures with novel geometries have become the subject of a large body of experimental and theoretical work [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Many of the fabricated structures exhibit curvature on the nanoscale making once purely theoretical investigations of quantum mechanics on curved and reduced dimensionality surfaces relevant to device modelling.…”

“…Many of the fabricated structures exhibit curvature on the nanoscale making once purely theoretical investigations of quantum mechanics on curved and reduced dimensionality surfaces relevant to device modelling. Because magnetic field effects prove important to Aharanov-Bohm and transport phenomena, the interplay of an applied field with the curved regions of a nanostructure [2,5,6,9,13,15,20,24,25] (particularly if the structure has holes) may be critical to a complete understanding of the physics of a nanodevice element.…”

“…In a previous work [6] the Schrodinger equation for an electron on a toroidal surface T 2 in an arbitrary static magnetic field was developed and numerical results obtained. There however, the electron was restricted ab-initio to motion on T 2 , which precluded the appearance of the well known geometric potential V C ∝ (h 2 − k), [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42] with h, k the mean and Gaussian curvatures, that arises via thin-layer quantization [43].…”

Spectral properties of two electrons vertically coupled in toroidal quantum rings

“…These facts allow us to manipulate the Coulomb interaction between particles and the Aharonov-Bohm (AB) [3] oscillations. In spite of the simplest model used to describe ring-like devices and quantum interference effects being based on one-dimensional rings [4][5][6], experimental studies [7] and theoretical calculations [8,9] with only one electron in a single toroidal QR [8] or concentric toroidal QRs [9] have revealed that the energy spectrum is strongly dependent on the shape and size of the QRs. The one-particle energy spectrum has been calculated by using the diagonalization method [8,9], while the energy structure of neutral and charged donors in a toroidal QR have been analyzed by using the variational method [10] or adiabatic approximation [11].…”