Exciton operators : commutation relations and dynamics

Abstract

The electron-hole pair operator commutation relations for a semiconductor are explicitly derived showing that the pairs are quasi-bosons with statistics intermediate between bosons and fermions. These pair operators are transformed into exciton operators, that incorporate the intra-pair Coulomb interaction, and it is found that the commutation relations remain quasi-bosonic. The exciton dynamics written in terms of the exciton operators are derived in the Heisenberg picture and compared with the traditionally used semiconductor Bloch equations.