Resonances of trion states in quantum dot molecules tuned by an electric field

The quantum states of the trion (two electrons and one hole X- or two holes and one electron X+) in double quantum dots are theoretically investigated within the effective-mass approximation for a quasi-one-dimensional model: the numerical method employed is exact in the sense that it does not rely on basis-set expansions nor on perturbative or variational approaches. We have investigated the tuning by the electric field of the energy levels into resonance showing crossing and anticrossing patterns. The ground and the excited states, for the spin-singlet and spin-triplet configurations, are calculated and discussed. The electric-field dependent spectra for the X- and X+ trions are similar, although they depend differently on the system parameters which define the confining potential. The oscillator strengths of the trion optical transitions are calculated for the first time for the double dot systems. For both types of trions, we found good agreement between calculations and the existing photoluminescence data obtained from vertically stacked double quantum dots. For a system of symmetric dots, we predict a parabolic dependence of the energy level of the triplet ground state on the electric field and substantially different patterns of the level anticrossings in the optical spectra.