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

Interactions and phase transitions on graphene's honeycomb lattice

The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semi-metal - antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and of the magnetic field are discussed.Comment: four pages, one figure; few typos corrected, references adde

Finite temperature superfluid density in very underdoped cuprates

The combination of a large superconducting gap, low transition temperature, and quasi two-dimensionality in strongly underdoped high temperature superconductors severely constrains the behavior of the ab-plane superfluid density \rho with temperature T. In particular, we argue that the contribution of nodal quasiparticles to \rho(T) is essential to account both for the amplitude of, and the recently observed deviations from, the Uemura scaling. A relation between T_c and \rho(0) which combines the effects of quasiparticle excitations at low temperatures and of vortex fluctuations near the critical temperature is proposed and discussed in light of recent experiments.Comment: 5 RevTex pages, 4 figures (one new); more discussion and comparison with experiment; version to appear in Phys. Rev.

Role of non-magnetic disorder on the stability of U(1) spin liquid : A renormalization group study

Recently Hermele et. al claimed that the infrared (IR) fixed point of non-compact $QED_3$ is stable against instanton excitations in the limit of large flavors of massless Dirac fermions [cond-mat/0404751]. We investigate an effect of non-magnetic disorder on the deconfined quantum critical phase dubbed U(1) spin liquid ($U1SL$) in the context of quantum antiferromagnet. In the case of weak disorder the IR fixed point remains stable against the presence of both the instanton excitations and non-magnetic disorder and thus the $U1SL$ is sustained. In the case of strong disorder the IR fixed point becomes unstable against the disorder and the Anderson localization is expected to occur. We argue that in this case deconfinement of spinons does not occur since the Dirac fermion becomes massive owing to the localization

Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z=1

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z=1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that the balance between the two may lead to charged quantum critical points at which z=1 exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions D=3-\epsilon. Precisely in D=3, however, the above simple result breaks down, and z>1. Relation to other theoretical studies is discussed.Comment: RevTex, 4 pages, 1 ps figur

Quantum critical scaling in magnetic field near the Dirac point in graphene

Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor f=1 in graphene we discuss the scaling of the interaction-induced gaps in vicinity of the Dirac point with the magnetic field. The gap at f=1 is shown to be bounded from above by E(1)/C, where E(n) are the Landau level energies and C = 5.985 + O(1/N) is a universal number. The universal scaling functions are computed exactly for a large number of Dirac fermions N. We find a sublinear dependence of the gap at the laboratory magnetic fields for realistic values of short-range repulsion between electrons, and in quantitative agreement with observation.Comment: 5 RevTex pages, 3 figures; added comments and references; cosmetic changes (this, published, version

Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene

Finite flux of the (time-reversal-symmetric) pseudo-magnetic field, which represents the effect of wrinkling of the graphene sheet for example, is shown to be a catalyst for spontaneous breaking of the time-reversal symmetry of Dirac fermions in two dimensions. Possible experimental consequences of this effect for graphene are discussed.Comment: 4 revtex pages; improved presentation, updated reference

Spectral Boundary of Positive Random Potential in a Strong Magnetic Field

We consider the problem of randomly distributed positive delta-function scatterers in a strong magnetic field and study the behavior of density of states close to the spectral boundary at $E=\hbar\omega_{c}/2$ in both two and three dimensions. Starting from dimensionally reduced expression of Brezin et al. and using the semiclassical approximation we show that the density of states in the Lifshitz tail at small energies is proportio- nal to $e^{f-2}$ in two dimensions and to $\exp(-3.14f\ln(3.14f/\pi e)/ \sqrt(2me))$ in three dimensions, where $e$ is the energy and $f$ is the density of scatterers in natural units.Comment: 12 pages, LaTex, 5 figures available upon request, to appear in Phys. Rev.

Conductivity of interacting massless Dirac particles in graphene: Collisionless regime

We provide detailed calculation of the a.c. conductivity in the case of 1/r-Coulomb interacting massless Dirac particles in graphene in the collisionless limit when \omega >> T. The analysis of the electron self-energy, current vertex function and polarization function, which enter into the calculation of physical quantities including the a.c. conductivity, is carried out by checking the Ward-Takahashi identities associated with the electrical charge conservation and making sure that they are satisfied at each step. We adopt a variant of the dimensional regularization of Veltman and t'Hooft by taking the spatial dimension D=2-\epsilon, for \epsilon > 0. The procedure adopted here yields a result for the conductivity correction which, while explicitly preserving charge conservation laws, is nevertheless different from the results reported previously in literature.Comment: 32 pages, no figures, published versio