Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
Starting from the graphene lattice tight-binding Hamiltonian with an on-site U and long-range Coulomb repulsion, we derive an interacting continuum Dirac theory governing the low-energy behavior of graphene in an applied magnetic field. Initially, we consider a clean graphene system within this effective theory and explore integer quantum Hall ferromagnetism stabilized by exchange from the long-range Coulomb repulsion. We study in detail the ground state and excitations at ν=0 and ν=±1, taking into account small symmetry-breaking terms that arise from the lattice-scale interactions, and also explore the ground states selected at ν=±3, ±4, and ±5. We argue that the ferromagnetic regime may not yet be realized in current experimental samples, which at the above filling factors perhaps remain paramagnetic due to strong disorder. In an attempt to access the latter regime where the role of exchange is strongly suppressed by disorder, we apply Hartree theory to study the effects of interactions. Here, we find that Zeeman splitting together with symmetry-breaking interactions can in principle produce integer quantum Hall states in a paramagnetic system at ν=0, ±1, and ±4, but not at ν=±3 or ±5, consistent with recent experiments in high magnetic fields. We make predictions for the activation energies in these quantum Hall states which will be useful for determining their true origin.
Additional Information© 2006 American Physical Society. (Received 3 May 2006; published 23 August 2006) We would like to thank Andrei Bernevig, Taylor Hughes, Allan MacDonald, and especially Leon Balents for stimulating discussions, as well as Philip Kim for sharing experimental data prior to publication. This work was supported by the National Science Foundation through Grants Nos. PHY-9907949 (M.P.A.F.) and DMR-0529399 (J.A. and M.P.A.F.).
Published - PhysRevB.74.075422.pdf
Submitted - 0604601.pdf