About the nature of the half-integer quantum features of transport and Hall resistance of 2D electron system in quantizing magnetic fields

It is shown that in two-dimensional (2D) electronic system in quantizing magnetic fields the coexistence of the electron-hole (excitonic) pairing due to the Coulomb interaction, on the one hand, and the Cooper pairing of 2D electrons due to their interaction with 2D phonons and 2D plasmons localized on the interface in semiconducting heterostructures, on the other hand, is possible. The critical temperatures of transition to excitonic and Cooper phases are obtained by summing up the divergent at T -> 0 - ladder type diagrams in the Cooper and zero sound channels. It is shown that the excitonic phase exists only in narrow regions nearby the half-integer values of the filling factor ν=(2n - 1)/2; n = 1, 2, 3, ..., in qualitative agreement with the experimentally observed anisotropic features in the transport resistance of 2D system in the integer Hall effect regime. The superposition of bound electron pairs and unpaired 2D electrons in the Cooper phase allows one to describe almost all the quantum features in the fractional Hall effect regime, including those values of n which cannot be described by the composite fermions model. At the same time the interelectron attraction can lead to a triplet Cooper pairing of composite fermions which is followed by the appearance of 'exotic' quantum features of the Hall resistance at ν=5/2. The arguments in favour of a possible experimental observation of the Cooper phase are presented