Bound exciton and hole: an exactly solvable three-body model in any number of dimensions

A three-body problem, concerning two holes in a nondegenerate valence band and a single electron in a conduction band, with strong short-range interactions, is solved exactly in any number of dimensions. The binding depends nontrivially on the ratio of the valence to conduction bandwidths (i.e., on the inverse ratio of their effective masses) and always vanishes when this ratio exceeds 1. The effective mass of the "trion" bound state also depends sensitively on this ratio and on dimensionality.