Effective interaction for charge carriers confined in quasi-one-dimensional nanostructures

A problem of interacting charge carriers confined in quasi-one-dimensional (1D) semiconductor nanostructures has been studied. We have derived an analytical 1D formula for the effective interaction potential between the confined charge carriers. We have applied both the 1D model with the effective potential and the full three-dimensional (3D) approach to an electron pair confined in a single and double quantum dot as well as to an exciton confined in a quantum wire. Comparing the results of the 1D and 3D approaches we have discussed the applicability of the effective 1D interaction potential to the real 3D nanostructures. We have shown that the present effective interaction leads to accurate results for weakly coupled multiple quantum dots and wire-like nanostructures, i.e., the quantum wires and dots with the lateral confinement much stronger than the longitudinal one.