Quantum Monte Carlo treatment of elastic exciton-exciton scattering

TL;DR

This paper presents a non-perturbative quantum Monte Carlo approach to calculate elastic exciton-exciton scattering cross sections, revealing spin-dependent effects and the possibility of diverging scattering lengths at certain mass ratios.

Contribution

It introduces a complete, non-perturbative Monte Carlo method for exciton scattering, providing new insights into spin effects and mass ratio dependencies.

Findings

Calculated scattering lengths for singlet and triplet excitons.

Identified spin-dependent differences in scattering cross sections.

Discovered conditions where the scattering length diverges or changes sign.

Abstract

We calculate cross sections for low energy elastic exciton-exciton scattering within the effective mass approximation. Unlike previous theoretical approaches, we give a complete, non-perturbative treatment of the four-particle scattering problem. Diffusion Monte Carlo is used to calculate the essentially exact energies of scattering states, from which phase shifts are determined. For the case of equal-mass electrons and holes, which is equivalent to positronium-positronium scattering, we find a_s = 2.1 a_x for scattering of singlet-excitons and a_s= 1.5 a_x for triplet-excitons, where a_x is the excitonic radius. The spin dependence of the cross sections arises from the spatial exchange symmetry of the scattering wavefunctions. A significant triplet-triplet to singlet-singlet scattering process is found, which is similar to reported effects in recent experiments and theory for excitons in quantum wells. We also show that the scattering length can change sign and diverge for some values of the mass ratio m_h/m_e, an effect not seen in previous perturbative treatments.