Electron interactions in graphene in a strong magnetic field

Graphene in the quantum Hall regime exhibits a multicomponent structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: The leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central $(n=0)$ rather than any other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant $a$ and magnetic length $l_B$ assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are lattice effects, algebraically small in $a∕l_B$. We analyze the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.

Figure 1

Effective interaction potentials in real space: Comparison between the relativistic (black lines) and nonrelativistic (gray lines) LLs $n=0$, 1, and 5. The dashed line represents the interaction potential in $n=0$, which is the same for relativistic and nonrelativistic electrons.