The Optical Excitonic Aharonov-Bohm Effect in a Few Nanometer Wide Type-I Nanorings

The optical excitonic Aharonov-Bohm effect in type-I three-dimensional (In,Ga)As/GaAs nanorings is theoretically explored. The single-particle states of the electron and the hole are extracted from the effective mass theory in the presence of inhomogeneous strain, and an exact numerical diagonalization approach is used to compute the exciton states and the oscillator strength $f_{x}$ for exciton recombination. We studied both the large lithographically-defined and small self-assembled rings. Only in smaller self-assembled nanorings we found optical excitonic Aharonov-Bohm effect. Those oscillations are established by anticrossings between the optically active exciton states with zero orbital momentum. In lithographically defined rings, whose average radius is 33 nm, $f_{x}$ shows no oscillations, whereas in the smaller self-assembled nanoring with average radius of 11.5 nm oscillations in $f_{x}$ for the ground exciton state are found as function of the magnetic field that is superposed on a linear dependence. These oscillations are smeared out at finite temperature, thus photoluminescence intensity exhibits step-like variation with magnetic field even at temperature as small as 4.2 K.