Solution to the excitonic problem of an electron in a quantum wire and a hole in a perpendicular 2D quantum layer

Abstract

We calculate the states of an exciton formed by an electron confined in a ID quantum wire (QW) and a hole confined in a 2D quantum layer (QL) perpendicular to the QW. The effective potential can be exactly calculated in the particular case where the confinement thicknesses are the same for the QW and QL. This effective potential can be used to calculate the exciton states for arbitrary confinement thicknesses, but here we show that in the limit of vanishing thickness the solution of our equation is very similar to the 3D bulk exciton equations, and therefore we can use these 3D exciton solutions as a basis for our system in a quantum perturbative approach.