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Renormalized transport properties of randomly gapped 2D Dirac fermions

We investigate the scaling properties of the recently acquired fermionic non--linear $σ$--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 $β$ function of the DC conductivity, computed for this model, is in perfect agreement with numerical results obtained previously.