Contact correlations of charged fermions in two dimensions and the electron-hole plasma lifetime in semiconductor quantum wells

Abstract

We consider a multicomponent ensemble of charged fermions which are constrained to move on the plane. By just retaining particle-particle ladder diagrams in Goldstone's expression for the energy shift and approximating the kernel of the resultant integral equation, we obtain for this system an analytical Yasuhara-like formula for the contact pair correlations that includes screening effects. An undesirable pseudo-screening due to the kernel approximation is overcome by adding a corrective term into the integral equation. In particular, we use the case in which the system has only two species of opposite charge to model a quantum well as a two-dimensional electron-hole plasma. The electron-hole correlation at contact so calculated is taken as the enhancement factor in the photoluminescence from the quantum well and it is checked against available experimental data for the density dependence of the electron-hole plasma lifetime.

Ladder approximation in coupled quantum-well systems

“…͑2͒ for electron-electron and electron-hole double-layer systems at equal density using matrix inversion techniques. In the previous applications 7,10,16 the bare Coulomb interaction appearing in the kernel was further approximated to obtain an analytical solution to the integral equation. Using the scaled quantities, our results will appear as independent of the electron-hole mass ratio m e /m h .…”

“…Even in the case of zero-thickness layers because of the presence of intralayer interactions, screening effects modify the pair-correlation functions at contact. This was noted by Pugnaloni, Melgarejo, and Vericat 16 where they replace the bare interaction V 12 (q) by V 12 (q)/(q) in the kernel of the integral equation. In fact, they introduce a phenomenological momentum cutoff to modify the integral equation to account for screening.…”

“…Since g eh (0) within the ladder approximation can be reliably calculated, the results agree quite well with the experimental data. 16,17 Similarly, the annihilation rate of positrons in an electronpositron two-component plasma is proportional to the contact pair-correlation function g ep (0). Although the selfconsistent field method of STLS has been analyzed 20,22 to include multiple scattering effects and therefore, leading to a bound state instability, the positivity condition for the paircorrelation functions within this formalism is usually hard to fulfill.…”

“…[8][9][10][11][12][13] Freeman 14 studied the correlation energy and antiparallel spin paircorrelation function of the two-dimensional electron gas within the particle-particle approximation of the coupledcluster equations making contact to the ladder approximation. Recently, an extension of the ladder theory to multicomponent systems were given in a series of papers by Vericat and Melgarejo, 15 Pugnaloni, Melgarejo, and Vericat 16 and Melgarejo et al 17 in connection with photoexcited electron-hole systems in quantum wells and quantum wires. We employ the multicomponent generalization of the ladder theory in application to double-layer electron-electron and electron-hole systems and particularly calculate the contact values of the pair-correlation function for these systems.…”

On-top pair-correlation function in the homogeneous electron liquid

“…In fact, investigations in this direction date back long ago, and a great deal of achievement has been made. [13,14,15,16,17,18,19,20,21,22] It is necessary here to give some introduction to the LT. The effective interaction V ef f (p, p ′ ; q) in the LT between two scattering electrons with respective momenta p and p ′ satisfies the following Bethe-Goldstone equation: [23] …”