We argue that massless Dirac particles in two spatial dimensions with 1/r Coulomb repulsion and quenched random gauge field are described by a manifold of fixed points which can be accessed perturbatively in disorder and interaction strength, thereby confirming and extending the results of arXiv:0707.4171. At small interaction and small randomness, there is an infra-red stable fixed curve which merges with the strongly interacting infra-red unstable line at a critical endpoint, along which the dynamical critical exponent z = 1.The properties of two dimensional massless Dirac fermions have recently sprung back into focus, largely due to the experimental discovery of the quantum Hall effect in graphene [1,2], the single layer graphite. Moreover, the ability to control the density of carriers by the electrical field effect allows experimental access to the rich physics of the neutrality point, where in the clean non-interacting picture, the conduction and the valence bands touch. It is well known [3] that, at the neutrality point, the exchange self-energy gives a logarithmic enhancement of the Fermi velocitywhere k is a small wavevector near the nodal point[3] and ǫ d is the dielectric constant of the medium. Physically, this effect is due to the lack of screening of the 1/r Coulomb interaction, an important consequence of which is the suppression of the single particle density of states (N (E)) at low energies. This in turn leads to the suppression of the electronic contribution to the low temperature specific heat [4].This suppression of N (E) may lure one into the (incorrect) conclusion that, at T = 0, the Coulomb interactions turn the clean system into an electrical insulator. However, the vertex corrections contribute an exactly compensating enhancement of the conductivity [5], making the system a metal with its residual conductivity asymptotically equal to the non-interacting value σ 0 = (π/8)e 2 /h per node.In this work, we analyze the effects of the unscreened Coulomb interactions and the quenched random gauge disorder beyond leading order in the perturbative renormalization group (RG) of Ref.[5]. Our principle findings, which support and extend those of Ref. [5] are twofold: first, in the clean case, there is an unstable fixed point at finite strength of Coulomb interactions characterized by the dimensionless ratio α = e 2 /( ǫ d v F ) which represents a quantum critical point (QCP) separating the semimetal from an excitonic insulator; and second, the interplay between Coulomb interactions and disorder induces a downward curvature of the fixed line [5,6], causing it to end at the clean QCP (see Fig.1).In two dimensions, the Hamiltonian for Coulomb interacting massless Dirac fermions in the presence of aThere is a line of stable fixed points at small ∆ and small α which merges with the line of unstable fixed points at the critical end point. The (clean) unstable fixed point at αc corresponds to a quantum phase transition into an excitonic insulator. Above the critical ∆ * , the disordered but non-interactin...

No abstract