A two-dimensional electron–hole system under conditions of fractional quantum hall effects

Abstract

It has been shown that the Chern–Simons (C–S) gauge field created by quantum point vortices under conditions of fractional quantum Hall effects (FQHEs) leads to the formation of composite electrons and holes with equal integer numbers of quantum point vortices attached to each particle. The coherent superposition of the velocities of these vortices leads to the formation of the C–S vector potential, which depends on the difference between density operators of the electrons and of the holes. The C–S vector potential generates an effective magnetic field acting on the particles in addition to the external magnetic field. In the mean field approximation, when the average densities of electrons and holes coincide, the effective C–S magnetic and electric fields vanish and the Landau quantization of the composite particles with the bare electron and hole effective masses take place only under the action of the external magnetic field.