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.

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.

Magneto-fermionic condensate under study is a Bose-Einstein condensate of cyclotron spin-flip magnetoexcitons in a quantum Hall insulator. This condensate features unique properties such as millisecond range lifetime and hundreds of micrometers of propagation length. In this study, utilizing the photo-induced resonant reflection technique, we measured the exciton escape time. Finally, we estimated the exciton condensate propagation velocity as 25 m/s, which is much higher than a single particle propagation velocity. We also proposed a mechanism of exciton condensation.

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.

Experimental results on the properties of a recently discovered new collective state, the magnetofermionic condensate, are summarized herein. Condensation occurs in a fermionic system, a quantum Hall insulator (filling factor nu = 2), as a result of the formation of a dense ensemble of long-lived spin cyclotron magnetoexcitons, composite bosons. At temperatures below 1 K, the exciton ensemble exhibits a sharp enhancement in its response to an external electromagnetic field due to the formation of a super-absorbing state that interacts coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level rearrange to form a new non-equilibrium radiative recombination channel. The condensate shows a sharp decrease in viscosity and the ability to spread over macroscopically large distances, on the order of a millimeter, at a speed of approximate to 103cms-1. Due to this rapid long-distance spin transfer, new opportunities in the field of spintronics have been opened up.

Three-particle complexes consisting of two holes in the completely filled zero-electron Landau level and an excited electron in the unoccupied first Landau level are investigated in a quantum Hall insulator. The distinctive features of these three-particle complexes are an electron-hole mass symmetry and the small energy gap of the quantum Hall insulator itself. Theoretical calculations of the trion energy spectrum in a quantizing magnetic field predict that, besides the ground state, trions feature a hierarchy of excited bound states. In agreement with the theoretical simulations, we observe new photoluminescence lines related to the excited trion states. A relatively small energy gap allows the binding of three-particle complexes with magnetoplasma oscillations and the formation of plasmarons. The plasmaron properties are investigated experimentally.

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.

New lines are observed in the photoluminescence spectrum of a two-dimensional electron gas in a quantizing magnetic field at a filling factor of ν = 2 upon the photoexcitation of a nonequilibrium ensemble of cyclotron magnetoexcitons. Their energies lie in the region forbidden for single-particle optical transitions and allowed for inner transitions from excited states of three-particle translationally invariant complexes called magnetotrions. It is suggested that the new lines are associated with the complicated spectrum of internal motion in the magnetotrion, composed of an electron at the first Landau level and two identical holes at the zeroth Landau level.

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