Interacting random Dirac fermions in superconducting cuprates

Electron localization properties in graphene

We study localization properties of the Dirac-like electronic states in monolayers of graphite. In the framework of a general disorder model, we discuss the conditions under which such standard localization effects as the logarithmic temperature-dependent conductivity correction appear to be strongly suppressed, as compared to the case of a two-dimensional electron gas with parabolic dispersion, in agreement with recent experimental observations.

Quantum critical fluctuations in disordered d-wave superconductors

To explain the strong quasiparticle damping in the cuprates, Sachdev and collaborators proposed to couple the system to a critically fluctuating id(xy)- or is-order parameter mode. Here we generalize the approach to the presence of static disorder. In the id case, the order parameter dynamics becomes diffusive, but otherwise much of the phenomenology of the clean case remains intact. In contrast, the interplay of disorder and is-order parameter fluctuations leads to a secondary superconductor transition, with a critical temperature exponentially sensitive to the impurity concentration.

Quasiparticle conductivities in disordered d-wave superconductors

We study the quasiparticle transport coefficients in disordered d-wave superconductors. We find that spin and charge excitations are generally localized unless magnetic impurities are present. If the system is close to a nesting point in the impurity-scattering unitary limit, the tendency towards localization is reduced while the quasiparticle density of states gets enhanced by disorder. We also show that the residual repulsive interaction among quasiparticles has a delocalizing effect and increases the density of states.

Nesting symmetries and diffusion in disordered d-wave superconductors

The low-energy density of states (DOS) of disordered 2D d-wave superconductors is extremely sensitive to details of both the disorder model and the electronic band structure. Using diagrammatic methods and numerical solutions of the Bogoliubov--de Gennes equations, we show that the physical origin of this sensitivity is the existence of a novel diffusive mode with momentum close to (pi,pi) which is gapless only in systems with a global nesting symmetry. We find that in generic situations the DOS vanishes at the Fermi level. However, proximity to the highly symmetric case may nevertheless lead to observable nonmonotonic behavior of the DOS in the cuprates.