Spatial correlation of electrons and holes in multiphonon resonant Raman scattering in a high magnetic field

Abstract

The role of spatial correlation between electrons and holes in the processes of resonant Raman scattering is studied through detailed analysis of a multiphonon Raman scattering in a high magnetic field which assumes the dominance of Fr\"ohlich interaction. We calculate the distribution ${\mathit{F}}_{\mathit{N}}$(r,K) of electron-hole pairs (EHP's) after emisson of a number of LO phonons as a function of the relative distance between an electron and a hole which were created by the incident radiation and gained the total wave vector K in the interaction with LO phonons. The scattering efficiency of the multiphonon resonant Raman scattering (MPRRS) of order N is proportional to the distribution function ${\mathit{F}}_{\mathit{N}}$(r=0,K=0) of EHP's with zero values of the relative distance and total wave vector. We show that the distribution of EHP's participating in the MPRRS process, in the plane perpendicular to the magnetic-field direction, is independent of both the electron--LO--phonon coupling and the number N of LO phonons being emitted and is determined by the magnetic-field strength only. The distribution along the magnetic field is written in a form reflecting the cascade character of the MPRRS with a series of transitions via real intermediate states that gives a clear qualitative picture of the process. By considering as an example the two LO-phonon scattering in a model involving heavy holes we show that the incoming resonance in the scattering intensity follows from the behavior of the EHP's concentration whereas the outgoing one results from the distribution function along the magnetic-field direction, thus underscoring the importance of spatial correlation between electrons and holes in the processes of resonant Raman scattering for the interpretation of experimental data.