Third-order optical response of intermediate excitons with fractional nonlinear statistics

Abstract

The interplay of exciton statistics and Coulomb interactions in the optical response of semiconductors is studied by derivation of an effective Hamiltonian written in terms of exciton operators, starting with a two-band model. Statistical effects are incorporated through the nonboson commutation relations of exciton operators, which contain an exciton-size-dependent parameter q that may vary from q = 0 (boson statistics) through q ≪ 1 (Wannier excitons) to q = 2 (Frenkel excitons or Pauli statistics). A unified Green’s function expression for χ(3) that applies to excitons of an arbitrary nature is derived.