Anomalous conductivity of two-dimensional Dirac electrons in organic conductor under pressures

The electric conductivity of Dirac electrons in the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene] under pressure has been examined using a two-dimensional tight-binding (TB) model with both impurity and electron--phonon (e--p) scatterings. We study an anomalous temperature dependence of the conductivity, which shows a crossover from $\sigma_{x} < \sigma_{y}$ at low temperatures [region (I)] to $\sigma_{x} > \sigma_{y}$ at high temperatures [region (II)]. $\sigma_y$ and $\sigma_x$ are diagonal conductivities parallel and perpendicular to a stacking axis of molecules, respectively. The effect of Dirac cone tilting is dominant in region (I), whereas the anisotropy of the velocity of the Dirac cone is dominant in region (II). Such behavior is further examined by calculating the deviation of principal axes due to the off-diagonal conductivity $\sigma_{xy}$ and a nearly constant conductivity at high temperatures due to the e--p scattering, which is the extension of the previous result of the simple two-band model [Phys. Rev. B {\bf 98},161205 (2018)]. The relevance to experiments of organic conductors is discussed.