A brief review of the current state of the theory of fractional quantum Hall effect (FQHE) is given along with the assumption of possible connection between the experimentally observed features of the Hall resistance of a two-dimensional electron system in a strong quantizing magnetic field for a fractional filling factor of the lowest Landau level with which cannot be described by the Laughlin wave function antisymmetric relative to pair transpositions, and the Cooper pairing of electrons. It is assumed that the electron–electron attraction essential for Cooper pairing can be due to the interaction of electrons with the surface acoustic waves phonons) and the surface plasmons localized near the crystal interfaces (heterojunctions) in the vicinity of inversion layers in the metal–insulator–semiconductor (MIS) structures and heterostructures. The coexistence of coupled electron pairs and unpaired electrons under the FQHE conditions must lead to peculiarities of for values of ν described by the Halperin relation following from the symmetry properties of the “mixed” wave function of pairs (bosons) and electrons (fermions). This relation makes it possible in principle to describe all experimental data on FQHE. The summation of “ladder” diagrams diverging according to a power law for leads to a Bethe–Salpeter-type equation for the vertex part of the electron–electron interaction for a system in a quantizing magnetic field taking into account electron–electron and electron–hole pairing in the Cooper and zero-sound channels. This equation is used to calculate the critical temperature of the phase transition to the state with coupled Cooper pairs and to prove that the value of in the ultra-quantum limit is independent of the effective mass of electrons, i.e., on the density of states. The phase diagram of the system is constructed for the variable electron concentration and magnetic field. It is shown that the region of Cooper pairing of electrons in the case of strong attraction almost coincides with the FQHE region for while the region of electron-hole pairing with the formation of charge-density waves (CDW) is expelled to the region with which is in accord with the experimental data concerning the CDW-induced features of the longitudinal resistance for with
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August 1999
Research Article|
August 01 1999
Cooper pairing of two-dimensional electrons in a quantizing magnetic field and the fractional quantum Hall effect
E. A. Pashitskiı̆
E. A. Pashitskiı̆
Institute of Physics, National Academy of Sciences of the Ukraine, 252650 Kiev, Ukraine
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Low Temp. Phys. 25, 690–701 (1999)
Citation
E. A. Pashitskiı̆; Cooper pairing of two-dimensional electrons in a quantizing magnetic field and the fractional quantum Hall effect. Low Temp. Phys. 1 August 1999; 25 (8): 690–701. https://doi.org/10.1063/1.593800
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