Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach

Abstract

We study the quantum Hall effect in graphene at filling factors \nu = 0 and \nu = \pm 1, concentrating on the quantum Hall ferromagnetic regime, within a non-perturbative bosonization formalism. We start by developing a bosonization scheme for electrons restricted to the lowest Landau level with two discrete degrees of freedom (spin-1/2 and pseudospin-1/2). Three distinct phases are considered, namely the so-called spin-pseudospin, spin, and pseudospin phases. The first corresponds to a quarter-filled (\nu =-1) while the others to a half-filled (\nu = 0) lowest Landau level. In each case, we show that the elementary neutral excitations can be treated approximately as a set of n-independent kinds of boson excitations. The boson representation of the projected electron density, the spin, pseudospin, and mixed spin-pseudospin density operators are derived. We then apply the developed formalism to the effective continuous model recently proposed by Alicea and Fisher. For each quantum Hall state, an effective interacting boson model is derived and the dispersion relation of the elementary excitations is analytically calculated. The possible effects of the boson-boson interaction term and the form of the charged excitations within this formalism are also briefly discussed.