Microscopic theory of the quantum Hall effect

The phonon exchange between the electron and the elementary magnetic flux (fluxon) induces an attractive transition in the degenerate Landau states. This attraction bounds an electron-fluxon complex. The center-of-mass of the complex moves as a boson with a linear dispersion relation (epsilon = cp). The 2D system of free massless bosons undergoes a Bose-Einstein condensation at k(B)T(C) = 1.954hcn(1/2), where n is the boson density. For GaAs/AlGaAs, T-C similar to 1 K at the principal Landau-level occupation ratio nu = 1, where the electron number equals the fluxon number. Below T-C , there is an energy gap, which stabilizes the Hall resistivity plateau. The plateau value (j/N)(h/e(2)) at the fractional occupation ratio nu = N/j, for odd j, indicates that the composite boson containing an electron and j fluxons carries the fractional charge (magnitude) e/j due to the magnetic confinement.