An exciton trapped by an arbitrary shaped nanoring in a magnetic field

We propose a simple method for calculating the energy spectrum of a magnetoexciton confined in a narrow infinite barrier planar quantum ring with a centreline of an arbitrary shape and a variable width. We show that in the adiabatic approximation the analysis of the low-lying levels of the exciton in such structure can be reduced to study of the angular two-particle motion. We present numerical results for energies of some low-lying levels in circular and elliptical quantum rings with weak variations in their widths as functions of the magnetic field strength. We show that variations in widths produce the quenching of the Aharonov-Bohm oscillations of the energy levels of the magnetoexciton.