Singular Density of States of Disordered Dirac Fermions in the Chiral Models

The Dirac fermion in the random chiral models is studied which includes the random gauge field model and the random hopping model. We focus on a connection between continuum and lattice models to give a clear perspective for the random chiral models. Two distinct structures of density of states (DoS) around zero energy, one is a power-law dependence on energy in the intermediate energy range and the other is a diverging one at zero energy, are revealed by an extensive numerical study for large systems up to $250\times 250$. For the random hopping model, our finding of the diverging DoS within very narrow energy range reconciles previous inconsistencies between the lattice and the continuum models.Comment: 4 pages, 4 figure

Kramers-Kronig relation of graphene conductivity

Utilizing a complete Lorentz-covariant and local-gauge-invariant formulation, we discuss graphene response to arbitrary external electric field. The relation, which is called as Kramers-Kr(\ddot{o})nig relation in the paper, between imaginary part and real part of ac conductivity is given. We point out there exists an ambiguity in the conductivity computing, attributed to the wick behavior at ultraviolet vicinity. We argue that to study electrical response of graphene completely, non-perturbational contribution should be considered.Comment: 7 page

Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene

We study 1-loop effects for massless Dirac fields in two spatial dimensions, coupled to homogeneous electromagnetic backgrounds, both at zero and at finite temperature and density. In the case of a purely magnetic field, we analyze the relationship between the invariance of the theory under large gauge transformations, the appearance of Chern-Simons terms and of different Berry's phases. In the case of a purely electric background field, we show that the effective Lagrangian is independent of the chemical potential and of the temperature. More interesting: we show that the minimal conductivity, as predicted by the quantum field theory, is the right multiple of the conductivity quantum and is, thus, consistent with the value measured for graphene, with no extra factor of pi in the denominator.Comment: 27 pages, no figures. Minor misprints corrected. Final version, to appear in J. Phys. A: Math. Ge

Density of states for the π\pi-flux state with bipartite real random hopping only: A weak disorder approach

Gade [R. Gade, Nucl. Phys. B \textbf{398}, 499 (1993)] has shown that the local density of states for a particle hopping on a two-dimensional bipartite lattice in the presence of weak disorder and in the absence of time-reversal symmetry(chiral unitary universality class) is anomalous in the vicinity of the band center $\epsilon=0$ whenever the disorder preserves the sublattice symmetry. More precisely, using a nonlinear-sigma-model that encodes the sublattice (chiral) symmetry and the absence of time-reversal symmetry she argues that the disorder average local density of states diverges as $|\epsilon|^{-1}\exp(-c|\ln\epsilon|^\kappa)$ with $c$ some non-universal positive constant and $\kappa=1/2$ a universal exponent. Her analysis has been extended to the case when time-reversal symmetry is present (chiral orthogonal universality class) for which the same exponent $\kappa=1/2$ was predicted. Motrunich \textit{et al.} [O. Motrunich, K. Damle, and D. A. Huse, Phys. Rev. B \textbf{65}, 064206 (2001)] have argued that the exponent $\kappa=1/2$ does not apply to the typical density of states in the chiral orthogonal universality class. They predict that $\kappa=2/3$ instead. We confirm the analysis of Motrunich \textit{et al.} within a field theory for two flavors of Dirac fermions subjected to two types of weak uncorrelated random potentials: a purely imaginary vector potential and a complex valued mass potential. This model is believed to belong to the chiral orthogonal universality class. Our calculation relies in an essential way on the existence of infinitely many local composite operators with negative anomalous scaling dimensions.Comment: 30 pages, final version published in PR