SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field

I consider the Hubbard model of graphene in an external magnetic field and in the Hartree-Fock approximation. In the continuum limit, the ground state energy at half filling becomes nearly symmetric under rotations of the three-component vector (N1,N2,m), with the first two components representing the Neel order parameter orthogonal to and the third component the magnetization parallel with the external magnetic field. When the symmetry breaking effects arising from the lattice, Zeeman coupling, and higher Landau levels are included the system develops a quantum critical point at which the antiferromagnetic order disappears and the magnetization has a kink. The observed incompressible state at filling factor one is argued to arise due to a finite third component of the Neel order parameter at these electron densities. Recent experiments appear consistent with vanishing N1 and N2, and finite N3, at the filling factors zero and one, respectively.Comment: 5 revtex pages: new figure, new eqs. 20-22, and the discussion of the experiment of Jiang et al added (v2). Cosmetic changes (v3). Accepted in PR

Explanation for the isotropy of the Dirac cone in graphene

It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of interacting electrons on honeycomb lattice are isotropic at low energies. The effect is due to the $Z_3$ subgroup of the $D_3$ symmetry group of the dispersion relation of Dirac quasiparticles. Consequences of the violations of the $Z_3$ or the sublattice symmetry are discussed.Comment: 2 RevTex pages; stylistic changes, published versio

Theory of integer quantum Hall effect in graphene

The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of Coulomb interaction on the scale of lattice constant. It is predicted that at a large in-plane component of the magnetic field such ordering will be present only at the filling factor |f|=1, and absent otherwise. Other experimental consequences of the theory are outlined.Comment: 5 pages, 2 figures, new paragraph on hierarchy of energy scales, new references, published versio

Theory of strongly phase fluctuating d-wave superconductors and the spin response in underdoped cuprates

General theory of d-wave quasiparticles coupled to phase fluctuations of superconducting order parameter is discussed. In the charge sector the superfluid density is found to conform to Uemura scaling, and the charge renormalization factor to decrease with underdoping. The spin susceptibilty exhibits four distinct regimes with increasing frequency and scales with the superconducting Tc, as observed.Comment: LaTex, 3 pages, proceedings of the M2S-HTSC conference in Rio, May 200