Para- and ortho-trions on a ring: A simple model

Motivated by recent experiments on luminescence from semiconductor nanoring s, we study theoretically the quantized states of a charged exciton (trion) in a ring geometry. In particular, we compare the energies of the states w ith antiparallel (para-trion) and parallel (ortho-trion) spin configuration s of two electrons, that, together with a hole, constitute a trion. In orde r to assess the experimentally relevant domain of parameters, when the size quantization energy is comparable to the exciton binding energy, we adopt a simple model of an infinitely narrow ring and short-range electron-electr on and electron-hole interactions.