Effective Hamiltonian for Excitons with Spin Degrees of Freedom

Details Effective Hamiltonian for Excitons with Spin Degrees of Freedom Effective Hamiltonian for Excitons with Spin Degrees of Freedom

1998-09-02

arxiv.org/abs/cond-mat/9809026v1

Physics

Condensed Matter

Materials Science

12 pages, no figures, RevTeX

Scientific paper

10.1143/JPSJ.67.3384

Starting from the conventional electron-hole Hamiltonian ${\cal H}_{eh}$, we derive an effective Hamiltonian $\tilde{\cal H}_{1s}$ for $1s$ excitons with spin degrees of freedom. The Hamiltonian describes optical processes close to the exciton resonance for the case of weak excitation. We show that straightforward bosonization of ${\cal H}_{eh}$ does not give the correct form of $\tilde{\cal H}_{1s}$, which we obtain by a projection onto the subspace spanned by the $1s$ excitons. The resulting relaxation and renormalization terms generate an interaction between excitons with opposite spin. Moreover, exciton-exciton repulsive interaction is greatly reduced by the renormalization. The agreement of the present theory with the experiment supports the validity of the description of a fermionic system by bosonic fields in two dimensions.

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