Novel Many-Body Procedure for Interacting Close-to-Boson Excitons

Abstract

It is well known that excitons are not exact bosons. However up to now, their close-to-boson character, which results from Pauli exclusion between their electrons and holes, has been extremely tricky to handle properly.

We have recently developed a “commutation technique” which allows to include the effects of Pauli exclusion in the exciton-exciton interactions exactly. This “Pauli way” for excitons to feel each other turns out to be as important as Coulomb interaction.

By using our commutation technique, we have already shown that:

• (i) The effective bosonic hamiltonian for excitons quoted by everyone up to now cannot be correct because it is not even hermitian. Purely “Pauli” terms are missing, which restore the hermiticity.

• (ii) Worse, one has to give up the concept of effective bosonic hamiltonian itself, since whatever the interacting terms are, they cannot generate the X-X correlations correctly.

• (iii) It is impossible to extract an exciton-exciton interacting potential from the semiconductor hamiltonian. As a major consequence, standard perturbative theories do not hold anymore: One has to invent novel many-body procedures from scratch. For instance, the Fermi golden rule is meaningless as well as the previous approaches to the X-X scattering rate.

• (iiii) The Mott criterion for disappearance of excitons based on Coulomb scattering is by two orders of magnitude less restrictive than the disappearance of the bosonic character of excitons based on Pauli exclusion.