Theory of the Half-integer Quantum Hall Effect in Graphene

Abstract

The unusual quantum Hall effect (QHE) in graphene is described in terms of the composite (c-) bosons, which move with a linear dispersion relation. The “electron” (wave packet) moves easier in the direction [1 1 0 c-axis] ≡ [1 1 0] of the honeycomb lattice than perpendicular to it, while the “hole” moves easier in [0 0 1]. Since “electrons” and “holes” move in different channels, the particle densities can be high especially when the Fermi surface has “necks”. The strong QHE arises from the phonon exchange attraction in the neighborhood of the “neck” surfaces. The plateau observed for the Hall conductivity and the accompanied resistivity drop is due to the superconducting energy gap caused by the Bose-Einstein condensation of the c-bosons, each forming from a pair of one-electron–two-fluxons c-fermions by phonon-exchange attraction. The half-integer quantization rule for the Hall conductivity: (1/2)(2P−1)(4e 2/h), P=1,2,..., is derived.