Disordered Fermi-Dirac distributions are used to model, within a straightforward and essentially phenomenological Boltzmann equation approach, the electron/hole transport across graphene puddles. We establish, with striking experimental support, a functional relationship between the graphene minimum conductivity, the mobility in the Boltzmann regime, and the steepness of the conductivity parabolic profile usually observed through gate-voltage scanning around the charge neutral point.
We derive an effective two-dimensional low-energy theory for thin superconducting films coupled to a three-dimensional fluctuating electromagnetic field. Using this theory we discuss plasma oscillations, interactions between charges and vortices and extract the energy of a vortex. Having found that the effective theory properly describes the long-distance physics, we then use it to investigate to what extent the superconducting film is a topologically ordered phase of matter.
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