Linear response peculiarity of a two--dimensional Dirac electron gas at weak scattering
arXiv:1309.4348 · doi:10.1103/PhysRevB.89.024201
Abstract
The conductivity of an electron gas can be alternatively calculated either from the current--current or from the density--density correlation function. Here, we compare these two frequently used formulations of the Kubo formula for the two--dimensional Dirac electron gas by direct evaluations for several special cases. Assuming the presence of weak disorder we investigate perturbatively both formulas at and away from the Dirac point. While to zeroth order in the disorder amplitude both formulations give identical results, with some very strong assumptions though, they show significant discrepancies already in first order. At half filling we evaluate all second order diagrams. Virtually none of the topologically identical diagrams yield the same corrections for both formulations. We conclude that a direct comparison of conductivities of disordered system calculated in both formulas is not possible.
Published version
References in corpus (8)
- Weak localisation magnetoresistance and valley symmetry in graphene
- Effect of Disorder on Transport in Graphene
- On the minimal conductivity of graphene
- On electron (anti)localization in graphene
- Random gap model for graphene and graphene bilayers
- Diffusion in the random gap model of mono- and bilayer graphene
- Long-range correlations in disordered graphene
- Dynamical symmetry breaking in a 2D electron gas with a spectral node