Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes

Abstract

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.

Dynamics in the quantum Hall effect and the phase diagram of graphene

“…However, as was pointed out in Ref. 17 (see also Refs. 19, 22, and 46), it is not exact for the Hamiltonian on the graphene lattice.…”

Artificial honeycomb lattices for electrons, atoms and photons

“…This AG system displays also an anomalous "spin-flip" mode ( Fig. 5c) that could arise from the removal of the sublattice-pseudospin degeneracy due to inter-site Coulomb repulsions [92]. Explorations of Hubbard excitations and anomalous spin-flip modes can be extended to molecular and photonic AG once interactions in these systems are turned on.…”

Edge states in graphene-like systems

“…At half filling, all possible combinations give C = 0, but it is possible to have C S = 2 if we fill the two LL with the same spin, and leave empty the other two. Interestingly, this spin-polarized filling can be driven by Coulomb interactions 72,79,91,92 and also by intrinsic spin-orbit coupling 93 .…”