New criteria for bosonic behavior of excitons

Dimensional arguments lead to say that N excitons in a sample of volume V behave as bosons for lambda Na-x(3)/V << 1, a(x) being the exciton radius and lambda a dimensionless factor. The Mott criterion, which is based on the disappearance of all exciton bound states because of screening, gives lambda similar or equal to1. Since excitons feel each other through both Coulomb interaction and Pauli exclusion between their electrons and holes, criteria based on the underlying fermionic character of the exciton should be even more relevant. Two significant quantities are the boson departure 1 - [B, B dagger] and boson number B daggerB, where B dagger is the exciton creation operator. Their expectation values in the N-exciton state are close to their boson values for lambda similar to 100 and lambda similar to 50, respectively. By contrast, the expectation value of B-N (B dagger)(N) in the vacuum state is close to N! for 25 N-2 a(x)(3)/V <<1 only. This surprising N-2-dependence comes from the intrinsic N-body character of Pauli exclusion. Consequences of these new criteria on the Bose condensation of excitons are discussed.