New quantum states in the fractional quantum Hall effect regime

Abstract

It is shown that the new fractional values of the filling factor observed experimentally in the fractional quantum Hall effect (FQHE) regime, ν=4/11, 4/13, 5/13, 5/17, 6/17, 3/8, and 3/10 (and also the complementary fractions 5/8 and 7/11), which do not fit the standard composite fermion model, can be described in the framework of an expanded systematics of the quantum states of the FQHE, based on Halperin’s conjecture of the coexistence of free electrons and bound electron pairs in two-dimensional (2D) systems in the thermodynamic limit. The possibility of existence of bound triplet “Cooper” pairs in a completely polarized state at the lowest spin Landau level may be due to the electron–phonon interaction of 2D electrons with 2D surface acoustic and optical phonons localized near the interface in semiconductor heterostructures. The proposed expanded systematics includes as particular cases the Laughlin model, the early hierarchical models of the FQHE, and the composite fermion model, including certain generalizations of it, and permits a description of absolutely all of the observed fractional values of ν, including fractions with even denominators (in particular, ν=3/8 and 3/10) and also predicts the possibility of existence of new “exotic” fractions (e.g., ν=5/14, 5/16, and 3/20).