Excitonic trions in single and double quantum dots

Excitonic trions in quantum dots with Gaussian confinement potential are studied by the variational method. We show that the photoluminescence line associated with the negative trion is always shifted towards lower energies with respect to the exciton line, and that this shift is larger for smaller dots. The qualitative behavior of the photoluminescence line of the positive trion is the same only in dots which resemble quantum wells or quantum wires. In other dots the size dependence of the positive-trion shift is more complex. In particular, we show that the order of the positive-trion line and the exciton line can be changed. The present approach has been generalized to the trion states in vertically coupled dots. We discuss the trion energy-level splitting induced by the coupling between the dots, as well as the relation between the photoluminescence-line shift with the binding energy of the trion in the double quantum dots.