On new quantum states in the regime of fractional quantum Hall effect

It is shown that the new fractional values of the filling factor nu 4/11, 4/13, 5/13, 5/17, 6/17, 3/8 , 3/10 (as well as the additional fractions 5/8 and 7/11) observed in the regime of fractional quantum Hall effect (FQHE), and not described by the standard model of composite fermions (CF) may be accounted for in the framework of an extended classification of quantum states of the FQHE. This new classification is based on the Halperin original idea on the coexistence of free electrons and coupled electron pairs in two-dimensional (2D) systems in the thermodynamic limit. The possibility of the existence of the coupled triplet Cooper pairs in the fully polarized state on the lowest Landau spin level arises from the electron-phonon interaction of 2D electrons with 2D surface acoustic and optical phonons, localized near the interface in the semiconducting heterostructures. The proposed extended classification includes, as individual cases, the Laughlin model, the early hierarchic models of the FQHE and the CF model with some of its generalizations, and describes absolutely all observed fractional values of n, including the fractions with even denominators (in particular, nu = 3/8 and 3/10). It also predicts the possibility of the existence of new 'exotic' fractional values (for example, nu = 5/14, 5/16, 3/20)