Temperature Dependence of the Dynamical and DC Conductivity in 2D Dirac Systems: Self-Consistent Random-Phase-Approximation Approach

We studied relaxation processes in heavily doped two-dimensional Dirac systems associated with electron scattering by acoustic and optical phonons and by static disorder. The frequency dependence of the real and imaginary parts of the relaxation function is calculated for different temperatures. The two-component low-frequency dynamical conductivity is found to be strongly dependent on temperature. At low temperatures, the imaginary part of the zero-frequency relaxation function and the DC resistivity are characterized by the scaling law aTx with the exponent x between 2.5 and 3.