Screening in a System of Many Particles Composed of Two Charged Fermions Application to Excitons

Abstract

A many-particle system of composite particles cohsisting of two different fermions each and interacting by the Coulomb potential is considered. For the case that the composites are present in bound states only the constituent self-energy is calculated to linear order in the density taking all symmetries of the many-body wavefunctions into account. The correlational part (screening part) of the selfenergy is calculated in the Born collision approximation. Numerical values for the shift of the continuum-edge of the spectrum of excitons in GaAs are presented.Es wird ein Vielteilchensystem untersucht, dessen Teilchen je aus zwei verschiedenen Fermionen mit Coulomb-Wechselwirkung zusammengesetzt sind. Fur den Fall, daB die Teilchen nur in Bindungszustanden vorliegen, wird ihre Selbstenergie linear in der Dichte unter Beriicksichtigung aller Symmetrien der Wellenfunktionen berechnet. Der Korrt:lations-(Abschirmungs-)beitrag zur Selbstenergie wird iq Bornscher Naherung untersucht. Numerische Werte fur die Absenkung der Kontinuumskante der Exzitonen in GaAs werden angegeben.

A kinetic equation for polaritons

“…by comparison with (26) of [ 7 ] ) that this self-energy is, in a sense, of excitonic RPA quality, not fully taking into account the composite nature of the excitons. Therefore, it may be improved on the lines of the discussion in [ 7 , 81.…”

Some Remarks on the Ground State of the Exciton and Exciton-Polariton System

“…It should be noted that the existence of a low density quantum fluid phase (the excitonic insulator) is very much an accident associated with the weak binding of biexcitons (otherwise a high density solid will transform into a high density plasma) and whether such a state exists in reality is not yet confirmed. There is by now at least very strong theoretical evidence from analytical [1,13] and numerical methods [15,16].…”

Many‐Body Theory for the Dense Exciton Gas of Direct Semiconductors II. Calculation of Exciton Level Shift and Damping in Dependence on Exciton Density

“…We write Z : : : : ) (according to (15) The most direct way of introducing expectation values would be the use of those wave functions which stand right from the energy denominator. However, @* of (A9) summed up with an arbitrary term of the 16 terms of @ can become divergent (Z 1@12 remains finite).…”

“…The sum rule for matrix elements of the dipole operator was used in [15]. This is most appropriate to the contributions t o Weff being quadratic in the Coulomb part of the exciton-exciton interaction potential.…”

“…The self-energy expression is identical with those obtained in [15] by means of a somewhat different technique. Extending the numerical evaluations of [15] we calculate beside the shift of the continuum edge also the shift and linewidth of the 1s exciton. This is done for an unrelaxed macro-occupation of the 1s exciton distribution and a relaxed (Boltzmann) distribution.…”