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Le Journal de Physique Colloques

EXCITONS AS A NEW QUANTUM SYSTEM

A. Mysyrowicz

Published Jul 1, 1980• 11 citations
Publisher

Abstract

In a first part, a brief review of some excitonic properties is presented, with the accent put on their relevance with respect to the possibility of Bose-Einstein condensation. In a second part, recent experimental evidence is described, which supports the idea that excitonic particles may form a highly quantum fluid. In Cu20, the analysis of the exciton decay spectrum shows a gradual evolution of the gas from a classical regime at low densities up to a strongly degenerate one at high densities, with a chemical potential µ ~ 0. In CuCl excitons are unstable against formation of molecules (biexcitons). It is possible to generate directly a high density gas of biexcitons with momentum K ~ 0 by giant two-photon absorption. At low excitation, the observed molecular emission is in agreement with Maxwell -Boltzmann statistics. At high densities, strong deviations occur. In particular, the appearance of a sharp emission line is attributed to the presence of a Bose-Einstein condensate of excitonic molecules.

DOI
10.1051/jphyscol:1980743

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In a first part, a brief review of some excitonic properties is presented, with the accent put on their relevance with respect to the possibility of Bose-Einstein condensation. In a second part, recent experimental evidence is described, which supports the idea that excitonic particles may form a highly quantum fluid. In Cu20, the analysis of the exciton decay spectrum shows a gradual evolution of the gas from a classical regime at low densities up to a strongly degenerate one at high densities, with a chemical potential µ ~ 0. In CuCl excitons are unstable against formation of molecules (biexcitons). It is possible to generate directly a high density gas of biexcitons with momentum K ~ 0 by giant two-photon absorption. At low excitation, the observed molecular emission is in agreement with Maxwell -Boltzmann statistics. At high densities, strong deviations occur. In particular, the appearance of a sharp emission line is attributed to the presence of a Bose-Einstein condensate of excitonic molecules.
The case of excitons as candidates for Bose–Einstein condensation is discussed, and experimental results in CuCl and Cu 2 O are presented. In CuCl, spectral analysis of the luminescence from biexcitons as a function of their density reveals a gradual evolution from classical statistics towards a quantum degenerate regime. The appearance of a sharp emission line below a critical temperature and above a critical density is attributed to the presence of a laser-induced Bose–Einstein condensate of excitonic molecules. This interpretation is supported by pump-probe experiments which show that additional particles injected in the presence of a biexciton condensate are drawn into it. In Cu 2 O, free exciton luminescence spectral analysis of ortho- and paraexcitons reveals a gradual evolution from a classical to a Bose quantum degenerate regime with increasing particle densities. Orthoexciton densities close to the critical density for condensation are obtained at high incoherent excitation. Under similar pumping, paraexciton densities exceeding the critical value are inferred from luminescence intensity ratios. Anomalous transport properties of paraexcitons, such as ballistic propagation over macroscopic distances and formation of soliton-like excitonic packets are discussed as evidence for excitonic superfluidity. Introduction Excitons The lowest electronically excited state of a non-metallic crystal corresponds to the promotion of one electron from the top of the highest fully occupied valence band to the bottom of the next empty conduction band. A correct evaluation of the required energy must include the Coulomb correlation between the promoted electron and all other electrons left behind in the valence band.
A comprehensive investigation of the optical properties of excitonic molecules in CuCl films is presented and discussed. The experimental work includes resonant two-photon absorption (TPA), observations of the resonantly excited biexciton emission, and optical pump-and-probe studies. The collision broadening of the TPA implies a collision rate \ensuremath{\sim}${10}^{\ensuremath{-}12}$ sec for the biexcitons, which is sufficiently rapid to establish a quasithermal equilibrium for the particles on a time scale that is short in comparison with the biexciton lifetime and the duration of the laser pump pulse. The biexciton luminescence line shapes obtained with resonant $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}=0$ two-photon excitation have been fitted using a Bose-Einstein thermal distribution of biexcitons. The chemical potential obtained from the fits goes to zero as the biexciton density is increased at a fixed lattice temperature or if the lattice temperature is decreased at fixed density. The sharp luminescence features that are observed at high densities and low temperatures with single-beam, two-photon excitation are interpreted as resulting from a Bose-Einstein---condensed state of the biexcitons at twice the wave vector of the laser pumping photons. Further evidence for a condensed state is obtained from optical-probe measurements in which a small number of probe biexcitons is injected into the sample, with and without the presence of a condensed state produced by an intense laser pump beam. The luminescence of these injected probe biexcitons is modified in the presence of the pump beam such that it exhibits the sharp features of the emission from the condensed state. Measurements of optical gain and stimulated emission in the presence of the pump beam show that the redistribution of the probe luminescence does not result from those processes, but must involve a preferential redistribution of the probe particles in momentum space via collisions. Such a redistribution is expected when additional particles are added to a condensed system of bosons.
Through the studies of excitation spectra of emissions in CuCl crystals by a frequency tunable dye laser, excitonic molecules have been found to be generated directly by the giant two-photon absorption at the photon energy of 3.187 eV, as suggested by Hanamura. Two-photon excitation of crystals at 1.6 K enhanced very narrow emission bands at 3.1647 eV and at 3.1709 eV. These photon energies coincide with those of the high energy edges of the M L and M T bands due to the radiative annihilation of excitonic molecules having K =0. From these facts the Bose condensation of excitonic molecules at K ∼0 has been suggested.
Great progress has been made in recent years in experimental studies of excitonic molecules, both in direct-band and indirect-band semiconductors. The exciton systems in these semiconductors differ substantially. In direct-band semiconductors with dipole-allowed optical transitions, the direct-recombination times are extremely small. Consequently the processes of binding of excitons into excitonic molecules and their decay occur under strongly nonequilibrium conditions. Hence one can obtain the fundamental information on biexcitons in these semiconductors by nonlinear optical methods. This review discusses the processes on which the various methods are based: two-photon resonance excitation of biexcitons, induced one-photon conversion of an exciton into a biexciton, two-photon resonance Raman scattering involving biexciton states, etc., and their application to studying biexcitons with the example of CdS. Problems of bistability involving biexcitons are also briefly discussed. In indirect semiconductors, where recombination occurs with the emission of a phonon, the lifetimes of excitons are large, and quasiequilibrium can be established in the exciton system. Under these conditions the information on the properties of the molecules is obtained by analyzing their radiative-decay spectra. The problem of detecting biexcitons in indirect semiconductors, radiative decay of molecules, and the effect on their stability of external electric, strain, and magnetic fields are discussed in detail with the examples of Si and Ge. Also the results of investigating the quantum statistical behavior of a dense gas of spin-oriented excitons (in a magnetic field under conditions in which the biexcitons are destabilized) are briefly presented (using the example of uniaxially compressed germanium), and the question of the possibility of their Bose condensation is discussed.
Experiments investigating the process of Bose-Einstein condensation of excitons in Cu2O will be reviewed. The exciton flux reaching the back surface of mm thick single crystals is investigated following creation of a high density of excitons close to the front surface with a pulsed laser. An anomalous propagation regime is observed at. sufficiently low crystal temperatures and sufficiently high particle densities, in the form of a ballistic packet progressing at a velocity close to the crystal sound velocity. The ballistic packet is attributed to an excitonic superfluid, the result of a Bose-Einstein Condensation (BEC). Conditions for appearance of the ballistic excitonic transport are found to be in good agreement with the predictions of the weakly interacting Bose gas model.
The Bose condensation of many exciton system is observed experimentally for the first time. It is found that excitonic molecules in CdSe exhibit the Bose condensation when the excitation is given at 1.8∼4.2 K by pico-second light pulses from a model-locked neodymium glass laser. This is concluded from the experimental facts that (1) an extremely sharp luminescence line attributed to originate from the k =0 condensed excitonic molecules is observed, (2) this sharp line is accompanied by the side-band on the low energy side and the spectrum is well understood by the theory developed by one of the authors, and (3) this line is produced within a limited range of excitation density which is wider at 1.8 K than at 4.2 K. Some arguments are presented on the importance of the use of the picosecond pulse excitation for the realization of the condensation.