Renormalized transport properties of randomly gapped 2D Dirac fermions

Abstract

We investigate the scaling properties of the recently acquired fermionic non--linear $\sigma$--model which controls gapless diffusive modes in a two--dimensional disordered system of Dirac electrons beyond charge neutrality. The transport on large scales is governed by a novel renormalizable nonlocal field theory. For zero mean random gap, it is characterized by the absence of a dynamic gap generation and a scale invariant diffusion coefficient. The $\beta$ function of the DC conductivity, computed for this model, is in perfect agreement with numerical results obtained previously.

Version published with minor changes

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• Quantum transport with strong scattering: Beyond the nonlinear sigma model
• Dynamical symmetry breaking in a 2D electron gas with a spectral node
• Two-parameter scaling theory of transport near a spectral node
• Finite-size scaling in a 2D disordered electron gas with spectral nodes
• Localization by particle-hole symmetry breaking: a loop expansion