Effective Hamiltonian for Excitons with Spin Degrees of Freedom

TL;DR

This paper derives an effective Hamiltonian for 1s excitons with spin, revealing interactions and renormalizations that align well with experimental observations, advancing understanding of excitonic systems with spin degrees of freedom.

Contribution

It introduces a projection-based derivation of the exciton Hamiltonian that accurately captures spin interactions and renormalization effects, improving upon simple bosonization methods.

Findings

Exciton-exciton interactions are significantly renormalized.

Opposite-spin excitons interact via generated terms.

The theory aligns well with experimental data.

Abstract

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.