Collective behavior of a spin-aligned gas of interwell excitons in double quantum wells

The kinetics of a spin-aligned gas of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructure) is studied. The temperature dependence of the spin relaxation time for excitons, in which a photoexcited electron and hole are spatially separated between two adjacent quantum wells, is analyzed. For this purpose, use was made of pulsed circularly polarized resonant photoexcitation of intrawell 1sHH excitons by a femtosecond frequency-controlled laser. A sharp increase in the spin-relaxation rate is observed for interwell excitons upon a change in temperature from 2 to 3.6 K. This effect is associated with indirect evidence of the coherence of the collective phase of interwell excitons at temperatures below the critical value.     

Interwell excitons in GaAs/AlGaAs double quantum wells and their collective properties

Luminescence spectra of interwell excitons in GaAs/AlGaAs double quantum wells with electric-field-tilted bands (n-i-n) structures were studied. In these structures the electron and the hole in the interwell exciton are spatially separated between neighboring quantum wells by a narrow AlAs barrier. Under resonant excitation by circularly polarized light the luminescence line of the interwell excitons exhibited appreciable narrowing as their concentration increased and the degree of circular polarization of the photoluminescence increased substantially. Under resonant excitation by linearly polarized light the alignment of the interwell excitons increased as a threshold process with increasing optical pumping. By analyzing time-resolved spectra and the kinetics of the photoluminescence intensity under pulsed excitation it was established that under these conditions the rate of radiative recombination increases substantially. The observed effect occurs at below-critical temperatures and is interpreted in terms of the collective behavior of the interwell excitons. Studies of the luminescence spectra in a magnetic field showed that the collective exciton phase is dielectric and in this phase the interwell excitons retain their individual properties.     

Phase diagram of the Bose condensation of interwell excitons in GaAs/AlGaAs double quantum wells

The luminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructures) with large-scale fluctuations of random potential in the heteroboundary planes was studied at low temperatures down to 0.5 K. The properties of excitons whose photoexcited electron and hole are spatially separated in the neighboring quantum wells by a tunneling barrier were studied as functions of density and temperature. The studies were performed within domains about one micron in size, which played the role of macroscopic traps for interwell excitons. For this purpose, the sample surface was coated with a metal mask containing special openings (windows) of a micron size or smaller. Both photoexcitation and observation of luminescence were performed through these windows by the fiber optic technique. At low pumping powers, the interwell excitons were strongly localized because of the residual charged impurities, and the corresponding photoluminescence line was nonuniformly broadened. As the laser excitation power increased, a narrow line due to delocalized excitons arose in a threshold-like manner, after which its intensity rapidly increased with growing pumping and the line itself narrowed (to a linewidth less than 1 meV) and shifted toward lower energies (by about 0.5 meV) in accordance with the filling of the lowest exciton state in the domain. An increase in temperature was accompanied by the disappearance of the line from the spectrum in a nonactivation manner. The phenomenon observed in the experiment was attributed to Bose-Einstein condensation in a quasi-two-dimensional system of interwell excitons. In the temperature interval studied (0.5–3.6) K, the critical exciton density and temperature were determined and a phase diagram outlining the exciton condensate region was constructed.     

Optical detection of an electric field in a GaAs/AlGaAs <Emphasis Type="Italic">n</Emphasis>-<Emphasis Type="Italic">i</Emphasis>-<Emphasis Type="Italic">n</Emphasis> heterostructure with double quantum wells

Processes occurring when a static transverse electric field is applied to a GaAs/AlGaAs n-i-n heterostructure with single quantum wells and asymmetric tunnel-coupled double quantum wells have been investigated by optical methods. The difference between the energies of exciton transitions for quantum wells of different widths makes it possible to attribute the observed photoluminescence peaks to particular pairs of wells or particular single quantum wells. The local electric field for each quantum well has been determined in terms of the Stark shift and splitting of exciton lines in a wide range of external voltage. A qualitative model has been proposed to explain the nonmonotonic distribution of the electric field over the depth of the heterostructure.     

Temperature dependence of luminescence intensity under Bose condensation of interwell excitons

Photoluminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructure) containing large-scale random potential fluctuations in the planes of heteroboundaries is studied. The properties of excitons, in which a photoexcited electron and a hole are spatially separated in neighboring quantum wells, were investigated upon variation of the power density of off-resonance laser excitation and temperature (1.5–4.2 K), both under lateral (in the heteroboundary plane) confinement of the excitation region to a few micrometers and without such a limitation (directly from the region of laser-induced photoexcitation focused to a spot not exceeding 30 μ. Under low pumping (with a power smaller than a microwatt), interwell excitons are strongly localized due to small-scale random potential fluctuations and the corresponding photoluminescence line is nonhomogeneously broadened to 2.5–3.0 meV. With increasing pumping power, the narrow line of delocalized excitons with a width of approximately 1 meV emerges in a threshold manner (the intensity of this line increases superlinearly near the threshold with increasing pumping). For a fixed pumping, the intensity of this line decreases linearly upon heating until it completely vanishes from the spectrum. The observed effect is attributed to Bose condensation in a quasi-two-dimensional system of interwell excitons. Within the proposed model, we show that the linear mode in the behavior of the luminescence intensity until its disappearance in the continuum of the photoluminescence spectrum upon a change in temperature is observed only for the condensed part of interwell excitons. At the same time, the luminescence of the above-the-condensate part of excitons is almost insensitive to temperature variations in the temperature range studied.     

Bose condensation of interwell excitons in lateral traps: A phase diagram

The luminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructures) containing large-scale random-potential fluctuations was studied. The study dealt with the properties of an exciton whose photoexcited electron and hole are spatially divided between the neighboring quantum wells under density variation and at temperatures of down to 0.5 K. We investigated domains ∼1 μm in size, which act as macroscopic exciton traps. Once the resonance laser pump power reaches a certain threshold, a very narrow delocalized exciton line appears (with a width less than 0.3 meV), which grows strongly in intensity with increasing pump power and shifts toward lower energies (by approximately 0.5 meV) in accordance with the exciton buildup in the lowest state in the domain. As the temperature increases, this spectral line disappears in a nonactivated manner. This phenomenon is assigned to Bose condensation occurring in the quasi-two-dimensional system of interwell excitons. The critical exciton density and temperature were determined within the temperature interval studied (0.5 to 3.6 K), and a phase diagram specifying the exciton condensate region was constructed. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 168–170. Original Russian Text Copyright ? 2004 by Dremin, Larionov, Timofeev.     

Bose condensation of interwell excitons in double quantum wells

The luminescence of interwell excitons in double quantum wells GaAs/AlGaAs (n-i-n heterostructures) with large-scale fluctuations of random potential in the heteroboundary planes was studied. The properties of excitons whose photoexcited electron and hole are spatially separated in the neighboring quantum wells were studied as functions of density and temperature within the domains on the scale less than one micron. For this purpose, the surfaces of the samples were coated with a metallic mask containing specially prepared holes (windows) of a micron size an less for the photoexcitation and observation of luminescence. For weak pumping (less than 50 μW), the interwell excitons are strongly localized because of small-scale fluctuations of a random potential, and the corresponding photoluminescence line is inhomogeneously broadened (up to 2.5 meV). As the resonant excitation power increases, the line due to the delocalized excitons arises in a thresholdlike manner, after which its intensity linearly increases with increasing pump power, narrows (the smallest width is 350 μeV), and undergoes a shift (of about 0.5 μeV) to lower energies, in accordance with the filling of the lowest state in the domain. With a rise in temperature, this line disappears from the spectrum (T _c ≤ 3.4 K). The observed phenomenon is attributed to Bose-Einstein condensation in a quasi-two-dimensional system of interwell excitons. In the temperature range studied (1.5–3.4 K), the critical exciton density and temperature increase almost linearly with temperature.     

Collective behavior of interwell excitons in GaAs/AlGaAs double quantum wells

Photoluminescence spectra of interwell excitons in double GaAs/AlGaAs quantum wells (n-i-n structures) have been investigated (an interwell exciton in these systems is an electron-hole pair spatially separated by a narrow AlAs barrier). Under resonance excitation by circularly polarized light, the luminescence line of interwell excitons exhibits a significant narrowing and a drastic increase in the degree of circular polarization of photoluminescence with increasing exciton concentration. It is found that the radiative recombination rate significantly increases under these conditions. This phenomenon is observed at temperatures lower than the critical point and can be interpreted in terms of the collective behavior of interwell excitons.     

Exciton-exciton collisions and conversion of interwell excitons in GaAs/AlGaAs superlattices

The ratio of the densities of intra-and interwell excitons in a symmetric system of coupled quantum wells — a superlattice based on a GaAs/AlGaAs heterostructure — is investigated over a wide range of optical excitation power densities. Conversion of interwell excitons into intrawell excitons as a result of exciton-exciton collisions is observed at high exciton densities. Direct evidence for such a conversion mechanism is the square-root dependence of the interwell exciton density on the optical excitation level. The decrease in the lifetime of interwell excitons with increasing excitation density, as measured directly by time-resolved spectroscopy methods, confirms the explanation proposed for the effect. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 623–628 (25 April 1997)     

Collective state of interwell excitons in GaAs/AlGaAs double quantum wells under pulse resonance excitation

The time evolution and kinetics of photoluminescence (PL) spectra of interwell excitons in double GaAs/AlGaAs quantum wells (n-i-n structures) have been investigated under the pulse resonance excitation of intrawell 1sHH excitons using a pulsed tunable laser. It is found that the collective exciton phase arises with a time delay relative to the exciting pulse (several nanoseconds), which is due to density and temperature relaxation to the equilibrium values. The origination of the collective phase of interwell excitons is accompanied by a strong narrowing of the corresponding photoluminescence line (the line width is about 1.1 meV), a superlinear rise in its intensity, a long time in the change of the degree of circular polarization, a displacement of the PL spectrum toward lower energies (about 1.5 meV) in accordance with the filling of the lowest state with the exciton Bose condensate, and a significant increase in the radiative decay rate of the condensed phase. The collective exciton phase arises at temperatures T<6 K and interwell exciton densities n=3×10¹⁰ cm^?2. Coherent properties of the collective phase of interwell excitons and experimental manifestations of this coherence are discussed.     

Large-scale coherence of the bose condensate of spatially indirect excitons

The Bose condensation of spatially indirect (dipolar) excitons in a wide single quantum well in an electric field transverse to the heterolayers is analyzed. Voltage is applied between a metallic film on the surface (Schottky gate) and a conducting electron layer inside a heterostructure (integrated electrode). The excitation of dipolar excitons and observation of their luminescence are performed through circle windows in a metallic mask 5 μm in diameter. Excitons are collected in a ring lateral trap, which is formed along the window perimeter owing to the strongly inhomogeneous electric field. When the critical condensation conditions in pump and temperature are reached, a narrow line of dipolar excitons corresponding to the exciton condensate appears stepwise in the luminescence spectrum. Under these conditions, a spatially periodic structure of equidistant luminescence spots appears in the luminescence pattern that is observed through a window with a resolution of about 1 μm and is selected by means of an interference filter. An in situ optical Fourier transform of spatially periodic structures from the real space to the k space is derived. The resulting Fourier transforms reproducing the pattern of the luminescence intensity distribution in the far field exhibit the result of the destructive and constructive interference, as well as the fact that the luminescence is directed along the normal to the heterolayers. These results are consequences of the large-scale coherence of the condensed exciton state in the ring lateral trap. Direct measurements of double-beam interference from pairs of luminescence spots in the ring show that the spatial coherence length is no less than 4 μm. Such a large scale means that the experimentally observed periodic luminescence structures are described by a common wavefunction under the condition of the Bose condensation of dipolar excitons.     

Bose-einstein condensation of exciton polaritons in high-<Emphasis Type="Italic">Q</Emphasis> planar microcavities with GaAs quantum wells

Condensation of exciton polaritons in planar microcavities with GaAs/AlAs quantum wells in the active area has been studied. It has been found that an increase in the lifetime of polaritons up to ∼10–15 ps when the Q factor of a microcavity exceeds 7000 makes it possible to detect Bose-Einstein condensation of polaritons with a dominant (>90%) photon component. Condensation occurs under thermodynamically nonequilibrium conditions in lateral traps with diameters ∼10 μm formed due to long-range fluctuations of the polariton potential. The violet shift of the polariton emission line at the condensation threshold significantly exceeds the energy of the repulsive interaction between polaritons in the condensate. It has been shown that the shift is mainly due to a decrease in the oscillator strength of bright excitons in lateral traps, caused by the localization of photoexcited long-living dark excitons.     

Nonlinear optical absorption and optical rectification in near-surface double quantum wells: combined effects of electric, magnetic fields and hydrostatic pressure

The theoretical study of the combined effects of electric and magnetic fields and hydrostatic pressure on the nonlinear optical absorption and rectification is presented for electrons confined within an asymmetrical GaAs?Ga_1-x Alx As double quantum well. The effective mass, parabolic band, and envelope function approaches are used as tools for the investigation. The electric field is taken to be oriented along the growth direction of the heterostructure and the magnetic field is applied parallel to the interfaces of the quantum wells. The pressure-induced mixing between the two lowest conduction bands is considered both in the low and high pressure regimes. According to the results obtained it can be concluded that the nonlinear optical absorption and rectification coefficients depend in a non-trivial way on some internal and external parameters such as the size of the quantum wells, the direction of applied electric field, the magnitude of hydrostatic pressure, the stoichiometry of the wells and barriers, and the intensity of the applied magnetic field.     

Intrawell and interwell transfer of excitons in growth-interrupted quantum wells

Intrawell and interwell transfers of excitons are observed by a temperature-dependent continuous-wave photoluminescence study of growth-interrupted single quantum wells. The intrawell transfer among the interface localization areas suggests a thermodynamic equilibrium between energy relaxation via LO-phonon emission and thermal population via phonon absorption. Thermal population is dominant in wider wells while relaxation is clearly observable in a four-monolayer narrow well at low temperatures. Interwell transfer of excitons also occurs between two narrow wells.     

Resonant tunneling GaAs/AlGaAs quantum well structures for p-i-n photovoltaic cells

This study is devoted to the development of resonant-tunneling structures of quantum wells implementing resonant matching of lower subbands of size quantization in an electric field of the p-i-n junction of photovoltaic elements. The method for controlling the lower subband position in quantum wells by introducing a series of the tunnel-transparent barriers into a quantum well is proposed. The possibility of varying the level position in deep quantum wells in a wide range up to the continuous spectrum is demonstrated on a grown model structure; in this case, agreement between calculated and experimental subband positions is achieved.     

Dipolar Biexcitons in Lateral Traps in Si/SiGe/Si Heterostructures

Si/Si_1–xGe_x/Si heterostructures with large-scale (micrometer-size) lateral potential fluctuations at the upper SiGe/Si-cap heterointerface are grown. These potential fluctuations are caused by partial strain relaxation in the SiGe layer. Low-temperature photoluminescence (PL) spectra show that these fluctuations form lateral traps where photoexcited nonequilibrium charge carriers are accumulated and bind into dipolar excitons, which ultimately recombine. At temperatures below 6 K, a new narrow line with a width considerably less than that of the dipolar exciton PL line emerges in the spectra as the level of excitation increases. It is shown that this line is associated with the recombination of dipolar biexcitons in large-scale traps.     

Stimulated scattering of indirect excitons in coupled quantum wells: signature of a degenerate Bose-gas of excitons.

We observe and analyze strongly nonlinear photoluminescence kinetics of indirect excitons in GaAs/AlGaAs coupled quantum wells at low bath temperatures, > or = 50 mK. The long recombination lifetime of indirect excitons promotes accumulation of these Bose particles in the lowest energy states and allows the photoexcited excitons to cool down to temperatures where the dilute 2D gas of indirect excitons becomes statistically degenerate. Our main result--a strong enhancement of the exciton scattering rate to the low-energy states with increasing concentration of the indirect excitons--reveals bosonic stimulation of exciton scattering, which is a signature of a degenerate Bose-gas of excitons.     

Collective state in a bose gas of interacting interwell excitons

Experiments associated with direct observations of a collective state in a gas of interacting interwell excitons in GaAs/AlGaAs double quantum wells are discussed. The structures constitute Schottky photodiodes. In a metallic gate, circular windows of various sizes (diameters of 2 to 20 μm) are etched by means of electronic-beam lithography. Through these windows, the photoluminescence of interwell and intrawell excitons is excited and detected. A microscopic device allows the observation of the spatial structure of luminescence with a resolution of 1 μm through the windows of a sample placed in superfluid helium. Using optical interference filters, the spatial structure of the luminescence is analyzed selectively in the spectrum for interwell and intrawell excitons under the same experimental conditions. It is found that the photoluminescence of interwell excitons under certain conditions exhibits an axisymmetric spatial structure: along the perimeter of the windows through which the photoluminescence is observed, a regular ring pattern of equidistant bright spots of the luminescence of interwell excitons appears. This structure appears only above the photoexcitation power threshold and the number of equidistant bright spots in the ring increases with the pumping power. At high pumping powers, the structure of distinct periodic luminescence spots is smeared. At a fixed pumping power, the phenomenon exhibits explicit critical temperature dependence: the structure of regularly located luminescence spots is smeared at T > 4 K. Axisymmetric spatial configurations of equidistant luminescence spots are observed in windows of the diameters 2, 5, and 10 μm. For intrawell excitons, the spatial structure of luminescence is not observed under similar experimental conditions: the luminescence of intrawell excitons is spatially uniform in all the windows under investigation. The effect is a result of the collective behavior of interacting interwell excitons.     

Two-dimensional electron gas in double quantum wells with tilted bands

When a voltage is applied to double quantum wells based on AlGaAs/GaAs heterostructures with contact regions (n-i-n structures), a two-dimensional (2D) electron gas appears in one of the quantum wells. Under illumination which generates electron-hole pairs, the photoexcited holes become localized in a neighboring quantum well and recombine radiatively with the 2D electrons (tunneling recombination through the barrier). The appearance, ground-state energy, and density of the degenerate 2D electron gas are determined from the structure of the Landau levels in the luminescence and luminescence excitation spectra as well as from the oscillations of the radiative recombination intensity in a magnetic field with detection directly at the Fermi level. The electron density is regulated by the voltage between the contact regions and increases with the slope of the bands. For a fixed slope of the bands the 2D-electron density has an upper limit determined by the resonance tunneling of electrons into a neighboring quantum well and subsequent direct recombination with photoexcited holes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 11, 840–845 (10 June 1997)     

Interwell exciton relaxation in semimagnetic asymmetric double quantum wells

The possibility of magnetic field control of the spectral and polarization characteristics of exciton recombination is examined in Cd(Mg, Mn) Te-based asymmetric double quantum wells. At low fields, the exciton transition in a semimagnetic well is higher in energy than that in a nonmagnetic well and the interwell exciton relaxation is fast. In contrast, when the energy order of the exciton transitions reverses at high fields, unexpectedly slow relaxation of σ⁻ polarized excitons from the nonmagnetic well to the σ⁺-polarized ground state in the semimagnetic well is observed. Strong dependence of the total circular polarization degree on the heavy-light hole splitting Δ _hh-lh in the nonmagnetic well is found and attributed to the spin dependent interwell tunneling controlled by exciton spin relaxation. Such a slowing down of the relaxation allows separation of oppositely spin-polarized excitons in adjacent wells. The text was submitted by the authors in English.