Role of acoustic phonons in exotic conductivity of two-dimensional Dirac electrons

We examine the effect of acoustic phonon scattering on the conductivity of two-dimensional Dirac electrons. The temperature ($T$) dependence of the conductivity ($\sigma$) is calculated using the electron Green's function with damping by both the impurity ($\Gamma_0$) and phonon ($\Gamma_{\rm ph}$).For zero or small doping, on which the present Rapid Communication focuses, $\sigma (T)$ increases and becomes almost constant due to the competition between the Dirac electrons and the phonon scattering. Such strange behavior of $\sigma (T)$ is ascribed to an exotic mechanism of phonon scattering, whose momentum space is strongly reduced in the presence of a Dirac cone. For large doping, $\sigma$ decreases due to the interplay of the Fermi surface and the phonon. The unconventional $T$ dependence of the resistivity $\rho (=1/\sigma)$ for small doping is compared with that of the experiment of Dirac electrons in an organic conductor.