Trions in a periodic potential

The group-theoretical classification of trion states (charged excitons X+/- ) is presented. It is based on considerations of products of irreducible pr ojective representations of the two-dimensional translation group. For a gi ven BvK period N degeneracy of obtained states is N-2. Trions X+/- consist of two identical particles (holes or electrons), so the symmetrization of s tates with respect to particles transposition is considered. There are N(N1)/2 symmetric and N(N-1)/2 antisymmetric states. Completely antisymmetric states can be constructed by introducing antisymmetric and symmetric spin f unctions, respectively. Two symmetry-adapted bases are considered: The firs t is obtained from a direct conjugation of three representations, whereas i n the second approach the states of an electrically neutral pair hole-elect ron are determined in the first step. The third possibility, a conjugation of representations corresponding to identical particles in the first step, is presented elsewhere. (C) 2001 American Institute of Physics.