Abstract
We have analytically evaluated a quantum correction to the classical Boltzmann conductivity in a single graphene sheet. The effective-mass theory is applied to electronic states and we have collected contributions represented by maximally-crossed diagrams in perturbative expansions of the conductivity by Kubo formula. A logarithmic correction is obtained as is well-known for two-dimensional systems and, surprisingly, it turned out to be both positive and negative dependent only on the interaction-range of scatterers. For the system without symmetry-breaking terms the correction has a negative value due to the quantum interference which enhances the probability of backward scattering, and this phenomenon is called weaklocalization. On the other hand, the spin-orbit interaction which maintains time-reversal symmetry changes the correction into positive since destructive quantum interference is caused by the sign change of spinors by 2π rotation. Simple symmetry considerations lead to the fact that the correction should be negative for a graphene sheet since spin-orbit interaction is weak enough in a graphene sheet, but the situation is not so simple.
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