Fizika Nizkikh Temperatur: Volume 25, Number 8-9 (August 1999), p. 920-935 ( to contents , go back )
Cooper pairing of two-dimensional electrons in quantizing magnetic field and fractional quantum Hall effect
E. A. Pashitskii
Institute of Physics of National Academy of Sciences of Ukraine, Nauki ave. 46, Kiev 252650, Ukraine
(Received March 2, 1999 )
The paper reviews briefly the current state of the theory of fractional quantum Hall effect (FQHE). It is suggested that the experimentally observed features of the Hall resistance RH of the two-dimensional (2D) electronic system in a strong quantizing magnetic field with a fractional filling of the lowest Landau level n=q/(2n+1) (q³2), which cannot be described by the Laughlin antisymmetric wave function may be responsible for by the Cooper pairing of 2D electrons. It is assumed that the electron-electron attraction necessary for the Cooper pairing may be resulted from the interaction of 2D electrons with surface acoustic waves (2D phonons) and surface 2D plasmons localized near the crystal interfaces (heterojunctions) in the vicinity of the inversion layers in MOS and heterostructures. The coexistence of electron pairs and unpaired electrons in the FQHE regime should lead to the features in RH for the values of n described by the Halperin relation. The latter is determined by the symmetry properties of the "mixed" wave function of pairs (bosons) and electrons (fermions), and allows, in principle, to describe all the experimental data on FQHE. Summation of the power-law diverging (at T®0) ladder diagrams gives a Bethe-Solpeter-type equation for the vertex part of the electron-electron interaction in a 2D system in the quantizing magnetic field, accounting for the electron-electron and electron-hole pairings in the Cooper and zero-sound channels. This equation provides a critical temperature Tc of the phase transition to a state with the Cooper pairs, Tc in the ultra-quantum limit being independent of the effective mass of the electrons, that is of the density of states. A phase diagram of the 2D system is constructed for the variable electron concentration and magnetic field. It is shown that in the case of sufficiently strong attraction the region of Cooper pairing of 2D electrons practically coincides with the region of FQHE for n > 1, while the region of electron-hole pairing, bringing about the quantum charge-density waves (CDW), is displaced to a region of n > 1, in agreement with the experimental data on the CDW-induced features of the longitudinal resistance Rxx for n=(2n+1)/2 with n ³ 2.