A high-resolution large-aperture optical system is used to visualize the formation and spreading in real space of dense photoexcitation ensembles in integer and fractional quantum Hall dielectrics at filling factors ν = 2 and ν = 1/3. A comparative analysis is performed of the correlation between the transport properties and spatial coherence of these ensembles.

An Erratum to this paper has been published: https://doi.org/10.1134/S1062873824110029

A high-aperture optical system is used to visualize the spatial spreading of a dense ensemble of spin cyclotron magnetoexcitons in a quantum Hall dielectric at a filling factor ν = 2 (a state of the integer quantum Hall effect). It has been found that the ability to propagate in a nondiffusive manner over macroscopic distances is inherent not only to excitons with a momentum on the order of the reciprocal magnetic length, which form a coherent magnetoexciton condensate, but also to excitons with momenta close to zero.

Shear interferometry is used to study the coherent properties of a dense ensemble of triplet cyclotron magnetoexcitons in a quantum Hall dielectric near a filling factor of $$\nu = 2$$ . Compared to the gas of uncondensed magnetoexcitons, the magnetoexciton condensate formed at fairly low temperatures by nonresonant photoexcitation is found to have an increased degree of coherence. Its transverse coherence length reaches ~10 µm in order of magnitude. The fraction of the condensate can be as high as 20% of the total number of triplet magnetoexcitons.

A review of experimental studies of the properties of a recently discovered new coherent collective state, a magnetoexciton condensate, is presented. Condensation occurs at temperatures below 1 K in a Fermi system, a quantum Hall insulator (a filling factor of ν = 2), as a result of the formation of a dense ensemble of long-lived triplet spin cyclotron magnetoexcitons—composite bosons. The condensed phase interacts coherently with an external electromagnetic field and demonstrates the ability of fast nondiffusive propagation over macroscopic distances and high spatial coherence.

The spatial spreading of a dense ensemble of spin cyclotron magnetoexcitons in a quantum Hall insulator at the filling factor ν = 2 is visualized using an optical system with a high aperture ratio. It is found that nondiffusive propagation over macroscopic distances is characteristic not only of excitons with a momentum on the order of the reciprocal magnetic length, which form a coherent condensate of magnetoexcitons, but also of excitons with very low momenta. The nondiffusive propagation of magnetoexciton condensates in real space is accompanied by a huge threshold increase in the amplitude of light reflection from excitations. The possible explanations of the observed behavior are discussed.

Using a high-resolution optical system, we visualize and compare the real-space transport of the dense ensembles of photoexcitations in integer and fractional quantum Hall insulators at the filling factors ν=2 and ν=1/3. We analyze the correlation between the transport properties and spatial coherence of these ensembles.

Методами сдвиговой интерферометрии исследованы когерентные свойства плотного ансамбля триплетных циклотронных магнитоэкситонов в квантово-холловском диэлектрике вблизи фактора заполнения ν = 2. Обнаружено, что по сравнению с газом надконденсатных магнитоэкситонов магнитоэкситонный конденсат, формирующийся при достаточно низких температурах с помощью нерезонансного фотовозбуждения, отличается повышенной степенью когерентности: поперечная длина когерентности по порядку величины достигает ∼10мкм. Доля конденсата может достигать 20 % от полного числа триплетных магнитоэкситонов.

It is found that the thermalization of triplet spin-flip magneto-excitons in a quantum Hall dielectric is an unprecedentedly long process for translation-invariant nonequilibrium electronic systems. It is shown that a magneto-fermionic condensate, a state characterized by the ability to rapidly transfer spin over macroscopic distances, is formed by spin-flip excitons with generalized momenta on the order of the reciprocal magnetic length.

Matveevich Eliashberg, has turned 90. G M Eliashberg was born on July 26, 1930 in Leningrad. In 1947, he entered the Physical Faculty of Leningrad University and graduated with honors in 1952. Five years later, he worked at the Leningrad plant Krasny Khimik (Red Chemist), where he had been assigned on graduating from university. In 1959, GM Eliashberg entered the postgraduate course of the Physical-Technical Institute in Leningrad. That same year, he published a paper formulating the theory of the superconducting state occurring owing to electron±electron interaction through the crystal lattice oscillations. In this study, he wonderfully combined the J Bardeen, L Cooper, J Schrieffer theory of superconductivity that had appeared two years before, the field theoretical formulation of this theory developed at that time by Lev Gor'kov, and A B Migdal's theory of electron±phonon interaction in normal metals. Being the basis of the microscopic description of superconductivity, the Eliashberg theory became with time a well-developed part of modern condensed state physics. Different modifications of this theory are being actively examined in application to new classes of superconductors and other mechanisms of electron±electron attraction. The remarkable recent discovery of lithium hydride superconductivity at a temperature of 250 K and a pressure of several megabars is only one of the examples of such examinations. In 1961, GMEliashberg became a junior research worker at the Physical-Technical Institute. There, he carried out a number of studies of transport phenomena in Fermi liquid. He developed the technique of analytical continuation that allowed finding frequency dependences of kinetic quantities calculated using the temperature diagram technique. This approach is conventional and is invariably used in theoretical studies, sometimes even without mentioning the name of its author. After defending his candidate thesis in 1963, GM Eliashberg left Leningrad for Chernogolovka, where he began working at the theoretical department of a branch of the Institute of Chemical Physics and then from 1965 at the newly founded Institute of Theoretical Physics (now Landau Institute for Theoretical Physics), where he has been working till the present day. In 1972, G M Eliashberg became Doctor of Physical and Mathematical Sciences, and in 1990 he was elected a corresponding member and in 2000 a full member of the Russian Academy of Sciences. In Chernogolovka, GMEliashberg taught at theMoscow Institute of Physics and Technology, first at the chair of theoretical physics in Dolgoprudnyi and then at the chair of problems of theoretical physics at the Landau Institute. The educational process is always closely related to the teacher's personality. The scientific style of Eliashberg is known for a skillful mastery of complicated analytical methods remarkably combined with a precision of the physical statement of the problem. Intercourse with G M Eliashberg gave students not only facts and knowledge, but also scientific culture, while inculcating good manners and teaching lucidity of mind. B Ivlev, L Levitov, Yu Nazarov, and others are among his disciples. When at Chernogolovka, G M Eliashberg carried out a number of studies that remained significant for many years after. In 1965, he and L P Gor'kov formulated the theory of small metallic particles. Describing an ensemble of such particles with the Wigner±Dyson distribution, the authors arrived at a number of conclusions accessible for experimental verification and anticipating the results of mesoscopyÐ the contemporary theory of quantum properties of disordered metals. In the late 1960s ± early 1970s, G M Eliashberg together with L P Gor'kov developed a consistent theory of superconducting state kinetics and derived a nonstationary generalization of the Ginzburg±Landau equations. One of the most remarkable phenomena established by him here was the amplification of superconductivity by a high-frequency field. This work by G M Eliashberg made an impact on extensive Uspekhi Fizicheskikh Nauk 190 (9) 1007 ± 1008 (2020) Translated by M V Tsaplina PERSONALIA PACS number: 01.60.+q

We discuss spin excitations in a degenerate 2D electron gas in a perpendicular quantizing magnetic field: spin-wave and ‘Goldstone’ excitons in a quantum Hall ferromagnetic (filling factor ν = 1), and spin-cyclotron excitons in a quantum Hall insulator ( ν = 2). The latter exhibit record-setting long lifetimes, up to 1 ms, owing to which a transition to a basically new collective state, a magnetofermionic condensate, is observable at temperatures T < 1 K. The condensate’s properties may be explained in terms of a coherent state being formed due to the emergence of a dense ensemble of photoexcited long-lived spin-cyclotron excitons obeying Bose statistics in a nonequilibrium system of 2D fermions.

In a dilute gas of triplet magnetoexcitons, complete thermalization does not occur because the energy and momentum cannot be conserved simultaneously. Relaxation to the lowest energy state becomes possible owing to exciton—exciton scattering upon reaching a certain critical exciton density. Since thermalization times are extremely large, ensembles of magnetoexcitons are substantially nonequilibrium and consist of above-condensate magnetoexcitons with generalized momenta close to zero and magnetoexcitons at the energy minimum with momenta about the inverse magnetic length. It has been shown experimentally that the magnetoexciton density is transferred to long distances not by all magnetoexcitons, but by those whose momentum is close to the inverse magnetic length, ∼10 6 cm −1 , and these magnetoexcitons form a magnetofermionic condensate.

A fundamentally new collective state, namely, the magnetofermionic condensate, is discovered during photoexcitation of a sufficiently dense gas of long-lived triplet cyclotron magnetoexcitons in a twodimensional Hall insulator with a high electron mobility, a filling factor of ν = 2, and temperatures of T < 1 K. The condensed phase coherently interacts with an external electromagnetic field, exhibits superradiant properties in the recombination of correlated condensate electrons with heavy holes in the valence band, and spreads nondissipatively in the layer of a two-dimensional electron gas to macroscopical large distances, transferring an integer spin. The observed effects are explained in terms of a coherent condensate in a nonequilibrium system of two-dimensional fermions with a fully quantized energy spectrum, in which a degenerate ensemble of long-lived triplet magnetoexcitons obeying the Bose statistics is present.

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AbstractA fundamentally new collective state, namely, the magnetofermionic condensate, is discovered during photoexcitation of a sufficiently dense gas of long-lived triplet cyclotron magnetoexcitons in a twodimensional Hall insulator with a high electron mobility, a filling factor of ν = 2, and temperatures of T < 1 K. The condensed phase coherently interacts with an external electromagnetic field, exhibits superradiant properties in the recombination of correlated condensate electrons with heavy holes in the valence band, and spreads nondissipatively in the layer of a two-dimensional electron gas to macroscopical large distances, transferring an integer spin. The observed effects are explained in terms of a coherent condensate in a nonequilibrium system of two-dimensional fermions with a fully quantized energy spectrum, in which a degenerate ensemble of long-lived triplet magnetoexcitons obeying the Bose statistics is present.

Excitation of long-lived triplet magnetoexcitons in a Hall insulator (filling factor ν = 2) with a high mobility of electrons, at low temperatures, Т < 1 K, enabled to discover a new collective state − magnetofermionic condensate, that interacts coherently with an external electromagnetic field, exhibits superradiant properties and, owing to its low viscosity, spreads over the surface of the two-dimensional structure for macroscopically large distances.

The possibility of creating dense ensembles of spin excitons, transferring them to macroscopic distances on the order of hundreds of microns, and recording the appearance of these excitons in the region spatially remote from the excitation point by means of simple techniques of photoexcitation and space-resolved detection of photoluminescence of a two-dimensional electron gas in a GaAs/AlGaAs quantum well has been demonstrated.