UNTANGLING THE VALLEY STRUCTURE OF STATES FOR INTRAVALLEY EXCHANGE ANISOTROPY IN LEAD CHALCOGENIDES QUANTUM DOTS

We put forward a generalized procedure which allows to restore the bulk-like electron and hole wave functions localized in certain valleys from the wave functions of quantum confined electron/hole states obtained in atomistic calculations of nanostructures. The procedure is applied to the lead chalcogenide quantum dots to accurately extract the intravalley velocity matrix elements and the constants of the effective intravalley Hamiltonian of the exchange interaction for the ground exciton state in PbS and PbSe quantum dots. Our results suggest that intravalley parameters in PbS quantum dots are much more anisotropic than the ones in PbSe. Renormalization of the velocity matrix elements, forbidden band gap, valley and exchange splittings of exciton and exciton binding energy are also calculated.