Bose Condensation Of Excitons Research Articles

Harmonic-potential traps for indirect excitons in coupled quantum wells

We explain our method of creating an in-plane harmonic potential for indirect excitons in coupled quantum wells, which has been developed for experiments on Bose condensation of excitons in two dimensions, although this method may also be used for trapping a two-dimensional electron gas. The indirect excitons in our coupled quantum wells exhibit a Stark shift of over 60 meV and lifetime of approximately 100 ns when electric field is applied normal to the wells. The excitons also move in response to applied voltage as if they had charge, with an effective mobility of 800 ${\mathrm{cm}}^{2}/\mathrm{V}\mathrm{}\mathrm{s}.$ We find that the effects of screening of the electric field at high carrier density are very important for understanding the behavior of the excitons.

New method for detection of exciton Bose condensation using stimulated two-photon emission

Stimulated two-photon emission by Bose-condensed excitons accompanied by a coherent two-exciton recombination, i.e., by simultaneous recombination of two excitons with opposite momenta leaving unchanged the occupation numbers of excitonic states with nonzero momenta, is investigated. Raman light scattering accompanied by a similar two-exciton recombination (or generation of two excitons) is also analyzed. The processes under consideration can occur only if a system contains Bose condensate, therefore, their detection can be used as a new method to reveal Bose condensation of excitons. The recoil momentum, which corresponds to a change in the momentum of the electromagnetic field in the processes, is transferred to phonons or impurities. If the recoil momentum is transmitted to optical phonons with frequency $\omega_0^s$, the stimulated two-photon emission with the coherent two-exciton recombination leads to the appearance of a line at $2\Omega'-\omega$, where $\Omega'=\Omega-\omega_0^s$ and $\Omega$ is the light frequency corresponding to the recombination of an exciton with zero momentum. Formulas for the cross sections at finite temperatures are obtained for the processes under consideration. Our estimates indicate that a spectral line, corresponding to the stimulated two-photon emission accompanied by the coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu$_2$O.

Manifestation of exciton Bose condensation in induced two-phonon emission and Raman scattering

The unusual two-photon emission by Bose-condensed excitons caused by simultaneous recombination of two excitons with opposite momenta leaving the occupation numbers of excitonic states with momenta $\mathbf{p}\ensuremath{\ne}0$ unchanged (below coherent two-exciton recombination) is investigated. Raman scattering accompanied by the analogous two-exciton recombination (or creation) is also analyzed. The excess momentum equal to the change of the electromagnetic field momentum in these processes can be transferred to phonons or impurities. The processes under consideration take place if there is Bose condensation in the interacting exciton system, and, therefore, can be used as a method to reveal exciton Bose condensation. If the frequency of the incident light $\ensuremath{\omega}<2\ensuremath{\Omega}$ $(\ensuremath{\Omega}$ is the frequency corresponding to the recombination of an exciton with p=0), the coherent two-exciton recombination with the excess momentum elastically transferred to impurities leads to the appearance of the spectral line $2\ensuremath{\Omega}\ensuremath{-}\ensuremath{\omega}$ corresponding to the induced two-photon emission. In this case the anti-Stokes line on frequency $\ensuremath{\omega}+2\ensuremath{\Omega}$ also appears in the Raman spectrum. If $\ensuremath{\omega}>2\ensuremath{\Omega},$ there are both Stokes and anti-Stokes lines on frequencies $\ensuremath{\omega}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\Omega}$ in the Raman spectrum. The induced two-photon emission is impossible in this case. The spectral lines mentioned above have phonon replicas on frequencies $|\ensuremath{\omega}\ifmmode\pm\else\textpm\fi{}(2\ensuremath{\Omega}\ensuremath{-}n{\ensuremath{\omega}}_{0}^{s})|$ corresponding to the transmission of the excess momentum (partially or as a whole) to optical phonons of frequency ${\ensuremath{\omega}}_{0}^{s}$ $(n$ is an integer number). The quantitative estimation shows that the light corresponding to the coherent two-exciton recombination can be experimentally observed in ${\mathrm{Cu}}_{2}\mathrm{O}.$

Collective exciton magnetic polarons in quantum wells with semimagnetic barriers

A mechanism for exciton Bose condensation is suggested. We show that the interaction of localized exciton magnetic polarons (EMP's) can lead to the formation of a free collective exciton magnetic polaron (CEMP) able to move as a whole particle. Critical conditions for this transition and characteristics of the CEMP are found. We interpret the recent data on giant magnetic polaron mobility in ${\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{M}\mathrm{n}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ quantum wells [G. A. Balchin, C. D. Poweleit, and L. M. Smith, in Proceedings of the 23rd International Conference on the Physics of Semiconductors, edited by M. Scheffler and R. Zimmermann (World Scientific, Singapore 1996), p. 2055] as a manifestation of the free CEMP formation due to clusterization of long-living indirect EMP's.

Bose condensation of exciton magnetic polarons in semimagnetic quantum wells

We suggest a new mechanism of Bose condensation of excitons in a quantum well with semimagnetic barriers. Attraction of excitons is due to their exchange interaction with semimagnetic environment. The long exciton lifetime needed for formation of a condensed phase is provided due to exchange-induced displacement of the hole into one of the barriers leading to formation of a long-living spatially indirect state. The resulted condensed state is a collective exciton magnetic polaron.

Unusual Raman scattering by Bose-condensed excitons

Teh unusual Raman scattering by Bose-condensed excitons caused by simultaneous recombination (or creation) of two excitons is investigated. It is shown that this scattering takes place only in the Bose-condensed interacting exciton system and is accompanied by the simultaneous recombination (or creation) of two excitons with equal and opposite momenta leaving the occupation numbers of excitonic states with p ≠ 0 unchanged. If ω > 2Ω, it is accompanied by the appearance of Stokes and antiStokes lines on frequencies ω ± 2Ω in the Raman scattering spectrum of the system (ω is the frequency of the incident light, Ω is the frequency corresponding to the recombination of an exciton with zero momentum). If ω < 2Ω, the line on frequency ω + 2Ω corresponding to the Raman scattering and the line on frequency 2Ω − ω corresponding to the induced two-photon emission caused by simultaneous two-exciton recombination appear. The quantitative estimation shows that both the Raman scattering and the induced two-photon emission can be detected experimentally and, therefore, can be used as a new method to reveal Bose condensation of excitons.

Kondo Insulator:p-wave Bose Condensate of Excitons

In the Anderson lattice model for a mixed-valent system, the $d\ensuremath{-}f$ hybridization can possess a $p$-wave symmetry. The strongly correlated insulating phase in the mean-field approximation is shown to be a $p$-wave Bose condensate of excitons with a spontaneous lattice deformation. We study the equilibrium and linear response properties across the insulator-metal transition. Our theory supports the empirical correlation between the lattice deformation and the magnetic susceptibility and predicts measurable ultrasonic and high-frequency phonon behavior in mixed-valent semiconductors.

Production of coherent states of excitons in semiconductors by means of the recombination of free carriers

It is shown that the modern experimental techniques make it possible to produce a coherent Bose condensate of excitons in semiconductors by the direct recombination of electrons from the conduction band and holes from the valence band.

Theory of optical spectra of exciton condensates.

We present theoretical calculations of optical absorption-gain spectra for condensed excitons in both three dimensional (3D), 2D, and quasi-2D systems (appropriate for semiconductor quantum wells) as functions of the electron-hole pair density and temperature. The ladder diagram contribution to the vertex function (exciton effect) is included in our calculation. We found that fluctuations cannot destroy the condensation of excitons in 2D at finite temperatures as opposed to a theory of free bosons and the case of Cooper pairs in superconductivity. Such a difference is attributed to the fact that electrons and holes carry opposite charges as opposed to the same charges carried by the Cooper pairs in the case of superconductivity. Our studies show that the effects of exciton Bose condensation on the absorption-gain spectra remain present for temperatures up to 130 K for a 2D system with exciton binding energy of 30{endash}40 meV (appropriate for ZnSe systems). {copyright} {ital 1996 The American Physical Society.}

Photoinduced Fermi‐edge singularity in one‐dimensional semiconductors

AbstractA high‐density electron–hole system in one dimension (1D) is studied theoretically in terms of the photoinduced Fermi‐edge singularity (FES) in optical spectra, the anomaly of which results from the fluctuating exciton Bose condensation in 1D. Describing this system as the two‐band Tomonaga Luttinger (TL) liquid with the forward‐scattering correlations, the critical exponent of the FES is analytically obtained with the aid of the bosonization technique. Competition between the exciton condensation and other Fermi‐surface instabilities is also clarified within the framework of the two‐band g‐ology. Comparison with the FES in ordinary 1D conductors (heavily‐doped 1D semiconductors), which are described as the single‐band TL liquids, is made to clarify recoil effects of an optical hole on the FES. Effects of backward scatterings, random potentials, spin‐dependent electronic correlations, and spin splitting of the conduction band are also discussed.

Bose condensation and superfluidity of excitons in a high magnetic field.

In a high magnetic field, such that the distance between the Landau levels exceeds the binding energy of an exciton, an exciton gas in a semiconductor is capable of forming the Bose-Einstein condensate as well as a superfluid state even at a relatively high temperature. We consider the problem of excitonic interaction in a semiconductor in its multielectron formulation, starting from the second-quantization representation of the Hamiltonian of interacting electrons and holes in a high magnetic field. The expressions for the ground-state energy, the chemical potential, and the spectrum of elementary excitations of the system are obtained in a linear approximation in the concentration of excitons. It is shown that a system of excitons in a high magnetic field is similar to a weakly nonideal Bose gas. The existence and the stability of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field are established at a high density of excitons. The results obtained show that the excitation spectrum vanishes linearly, with a slope equal to a macroscopic speed of sound which depends on the direction of the magnetic field. Thus this spectrum satisfies the Landau criterion for superfluidity. The possible observable effects of the Bose condensate and the superfluidity of excitons in a high magnetic field are also discussed. It is shown that Bose condensation leads to unusual optical properties of a semiconductor, e.g., anomalous absorption of light, and to another mechanism of light amplification.

Superfluidity of excitons in a high magnetic field.

In a high magnetic field, such that the distance between the Landau levels exceeds the exciton Rydberg, the triplet interaction term becomes the lowest state of the system. Under these circumstances, a weak pair interaction in the triplet ground state opens a new opportunity to forming the Bose-Einstein condensate and a superfluid state of excitons at a relatively high temperature. The existence of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field are established. We show that the excitation spectrum satisfies the Landau criterion for superfluidity, and discuss the observable effects of the Bose condensate of excitons.

Four-wave mixing signatures of exciton Bose condensation

We propose a transient grating experiment in order to observe exciton Bose condensation. We show that for typical parameters in semiconductors the velocities of first and second sound are comparable, resulting in a characteristic behavior of the decay of the longitudinal modes.

Electron-hole system in one dimension

A high-density electron-hole system in one dimension is studied theoretically. Competition between the exciton Bose condensation and other Fermi-surface instabilities is clarified within a framework of the two-band g-ology. There is a parameter region where unconventional interband Cooper pairing with nonzero total momentum occurs. Optical spectra yield the Fermi-edge singularity resulting from the exciton condensation. Effects of backward scattering and random potential are also discussed.

Transient grating spectroscopy of exciton sound waves in dense exciton fluids

A dynamic description is developed for the motion of an exciton fluid at high exciton density. Coherent oscillatory modes of the exciton density are predicted provided the exciton—phonon coupling is dufficiently small. The physical mechanism is similar to that of sound waves in an ordinary gas. A method to probe these motions using transient grating with strong pump fields is proposed. The grating recurrence time is estimated to be about 100 ps for typical molecular crystals. Exciton Bose condensation could also be probed using the same technique.

Possibility of coherent light emission from Bose condensed states in quantum-well systems

The possibility of coherent light emission in systems with a pairing of electrons and holes in a double quantum well spatially separated by a thin barrier (separated electron hole pairs (SEHPs)) is predicted. Bose condensation of excitons formed from SEHPs in GaAs/Al/sub x/Ga/sub (1-x)/As double quantum wells of approximately 10 AA size are possible at relatively high temperatures. Coherent recombination emission due to the transfer of coherence from the Bose-condensed SEHPs to the photon field is expected. >

Possibility of coherent light emission from Bose condensed states of SEHPs

The possibility of Bose condensation of excitons has been predicted in a system with spatially separated electron hole pairing (SEHP), e.g. a GaAs/AlGaAs double quantum well separated by a thin quantum barrier. Coherent recombination emission has been expected, due to the transfer of coherence from the condensed excitons to the photon field.

Possibility of Bose condensation of excitons in a size-quantized semiconductor disc

Within the framework of a very simple model the size-quantization effect on cooperative features of excitons in a semiconductor disc is taken into account. It is shown that because of the energy quantization of the translational motion of excitons in the latter subsystem the onset of the Bose condensation turned out to be possible at temperature different from zero. With an increasing disc radius the transition temperature tends to zero monotonically.

Feasibility of the Bose Condensation of Excitons in a Quantizing Semiconductor Sphere

physica status solidi (b)Volume 136, Issue 2 p. K105-K108 Short Note Feasibility of the Bose Condensation of Excitons in a Quantizing Semiconductor Sphere V. A. Haroutunian, V. A. Haroutunian Erevan State University Search for more papers by this authorE. M. Kazarian, E. M. Kazarian Erevan State University Search for more papers by this author V. A. Haroutunian, V. A. Haroutunian Erevan State University Search for more papers by this authorE. M. Kazarian, E. M. Kazarian Erevan State University Search for more papers by this author First published: 1 August 1986 https://doi.org/10.1002/pssb.2221360256 Mrajian 1, 375 049 Erevan, USSR. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume136, Issue21 August 1986Pages K105-K108 RelatedInformation

Is the ground state of the two-dimensional electron-hole fluid in a strong magnetic field an exciton Bose condensate or a maximum density pancake?

The 2D electron-hole fluid in a strong perpendicular magnetic field is studied. It is found that, in a III–V quantum well, two types of different ground states can exist, depending on the polarization of the pumping light: (i) a pancake of maximum local density or (ii) a Bose condensate of weakly repulsive magnetic excitons. This condensate is superfluid and moves, under application of an electric field, with the Hall velocity. The luminescence properties are also discussed.