Hole energy levels and effective g-factor of quantum rings utilizing k.p Hamiltonian in terms of cylindrical polar coordinates.

Abstract External fields effects on hole energies and effective g -factor of an infinite confining potential quantum ring are theoretically investigated. Based on envelope-function approach within the cylindrical polar coordinates, four band k ⋅ p method was used. We then derive the effective holes Hamiltonian and because of the ring geometry, we solve the problem as a 2-D grid (ρ , z) set of equations and finally valence band (VB) energy eigenvalues and g -factor of the system are estimated by using the finite difference method (FDM). Numerical results for different values of applied fields as well as various geometrical dimensions are presented. We find that our results are in good agreement with the results reported in experimental works. Our results highlight the role of external fields and the ring size for an accurate description of these two dimensional systems. Highlights • Kohn-Luttinger Hamiltonian for holes is derived within the cylindrical polar coordinates. • Fields effect on hole energy spectrum and g-factor confined in a QR are investigated. • Magnetic field has a great influence on hole energy spectrum and g-factor. • Energy eigenvalues are increased and effective g-factor remains almost constant with electric field. • Also the ring size considerably changes hole energy eigenvalues and g-factor. [ABSTRACT FROM AUTHOR]