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

Abstract

A brief review of the theory of the ground state properties of the electron-hole system is presented, discussing the full density regime from isolated excitons to the electron-hole plasma. Particular attention is devoted to a discussion of coherent condensed phases, especially when excitonic recombination allows the excitonic coherence to be transferred to the light field.

Prediction of an Excitonic Ground State inInAs/InSbQuantum Dots

“…The bi-excitonic ground state is similar to a helium atom in the sense that there are two positive and two negative Coulomb bound charges. These states can be identified as "excitonic molecule" states [4]. The calculated permanent electric dipole moment p = xρ(x)d 3 x for the exciton and bi-exciton of the lens-shaped dot D2 are aligned along (001) direction (growth direction), and amount to p z =3.58 eÅ for the exciton and p z =7.16 eÅ for the biexciton.…”

“…At medium and high densities, where the QDs have stronger coupling, there could be numerous phases as a function of carrier density and mass ratios, as proposed in Ref. 4. In these regions, the picture of (bi-)exciton on a single QD is not valid anymore.…”

“…an "excitonic ground state" as envisioned by Mott [1] and Keldysh et al [2]. Indeed, the electron-hole system exhibits a rich range of phases [3,4] as a function of the carrier density and effective-mass ratio m e /m h , including various excitonic insulating states such as molecular solid, exciton liquid, Mott insulator, and also various metallic phases. The excitonic ground state is of fundamental interest in itself because excitons can be a better alternative to atoms for studying Bose-Einstein condensation [5,6] on account of the lighter excitonic mass, thus higher condensation temperature.…”

Models of coherent exciton condensation

“…The electron-hole system is surely one of the simplest model systems in condensed matter physics. The ground state(s) of this model are likely to include various kinds of quantum solids and liquids [41]. The relevant parameters are the density (measured by r s ), the mass ratio of electron to hole Γ = m e /m h , and, for 2D bilayers, the separation d. If Γ ≫ 1, then we are discussing hydrogen, where we expect that the two basic phases are either a molecular solid of H 2 , or at very high densities a metallic crystal -where the electrons delocalise.…”

Optical recombination of biexcitons in semiconductors

“…Luminescence of these biexcitons, which are bound states of excitons (electron-hole pairs), is potentially relevant for studying luminescence from semiconductor lasers. While semiconductor lasers correspond to the dense limit of the electron-hole phase diagram, where the electrons and holes ionise into a plasma 1 , it is well known that the inclusion of correlation effects with the surrounding electrons and holes is necessary for a good estimate of semiconductor luminescence [2][3][4] . Moreover, a variational Monte Carlo study of the electron-hole phase diagram has revealed a surprisingly large excitonic insulator phase, which extends well into these high densities 5 .…”