V. B. Timofeev

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.

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.

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.

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 (Tc ≤ 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.

Condensation of interwell excitons in GaAs/AlGaAs double quantum wells

Experimental observations of the collective behavior of interwell excitons in the binary quantum wells with inclined bands under bias are discussed.

Long-range coherence of interacting Bose gas of dipolar excitons

Experiments connected with dipolar exciton Bose condensation in lateral traps are reviewed. Observations of long-range coherence of condensate in ring electrostatic traps in Schottky-diode heterostructures with double and single quantum wells are presented and discussed.

Interwell excitons in a lateral potential well in an inhomogeneous electric field

The luminescence of interwell excitons in double quantum wells based on GaAs/AlGaAs semiconductor heterostructures (n-i-n structures) in a lateral trap prepared with the use of an inhomogeneous electric field was studied at helium temperatures. A rather strong and inhomogeneous electric field occurred in the depth of the heterostructure when a current passed through the contact between the conducting tip of a tunneling microscope and the heterostructure surface to the bulk region containing a built-in gate. Because of the Stark shift of energy bands in the electric field, the photoexcited electrons and holes are spatially separated in neighboring quantum wells by a tunnel-transparent barrier and are bound into interwell quasi-two-dimensional excitons. These excitons have a dipole moment even in the ground state. Therefore, electrostatic forces in the inhomogeneous electric field cause the excitons to move in the plane of quantum wells toward the maximum field region and eventually accumulate in the lateral trap artificially prepared in such a way. The maximum trap depth achieved through the inhomogeneous electric field was 13.5 meV, and its lateral size was about 10 μm. It is shown that, in the traps prepared in this way, photoexcited interwell excitons behave with increasing concentration at sufficiently low temperatures (T=2K) in the same fashion as in the lateral traps caused by large-scale fluctuations of the random potential. At concentrations exceeding the percolation threshold, the interwell excitons condense into the lowest energy state in the trap.

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.

Linear polarization of luminescence in Bose-Einstein condensation of indirect excitons and spontaneous symmetry breaking

The linear polarization of luminescence from the Bose-Einstein condensate of dipolar (indirect) excitons accumulated in the ring lateral traps in GaAs/AlGaAs Schottky-diode heterostructures with a wide single quantum well has been observed. Luminescence from direct excitons remains unpolarized under the same experimental conditions. It has been shown that the linear polarization of the exciton condensate may arise from the anisotropic electron-hole (e–h) exchange interaction associated with the lateral anisotropy of the confining potential. The interaction mixes and splits the ground state of optically active excitons on heavy holes (with angular momentum projections of m=±1). The split spectral components from the corresponding angular momentum projections are linearly polarized in mutually orthogonal directions. Under this e–h exchange, the condensate component of excitons should appear in the lowest of the split states and luminescence from the Bose-Einstein condensate of excitons in such a split state becomes linearly polarized along the 〈110〉 crystallographic direction in the quantum well plane. The observed effect is a manifestation of spontaneous symmetry breaking in Bose-Einstein condensation of excitons.

Magnetooptics of the incompressible Fermi liquid and of the Wigner solid

Abstract We have studied the magnetic field dependence of the spectral position of the luminescence line due to radiative recombination of two-dimensional electrons in the extreme quantum limit. We verify the recent theoretical prediction that the spectral position of the line reflects the mean energy of the electrons and find downward cusps at fractional filling factors. From the strength of these cusps we derive values for the fractional quantum Hall effect gaps and their dependence on the magnetic field. We also investigate the influence of an electric field on the properties of the additional luminescence line which appears in the Wigner solid regime. We find a threshold enhancement of the intensity of this line, which is accompanied by an appearance of additional noise, which we associate with a sliding of the pinned Wigner solid by the electric field. Our results indicate that the melting of the Wigner solid occurs in two steps and can be characterized by two critical temperatures.