Electric Conductivity of the Zero-gap Semiconducting State in Alpha-(BEDT-TTF)2I3 Salt

The electric conductivity which reveals the zero gap semiconducting (ZGS) state has been investigated as the function of temperature $T$ and life time $\tau$ in order to understand the ZGS state in quarter-filled $\alpha$-(BEDT-TTF)${}_2$I${}_3$ salt with four sites in the unit cell. By treating $\tau$ as a parameter and making use of the one-loop approximation, it is found that the conductivity is proportional to $T$ and $\tau$ for $k_B\gg \mathrm{\hslash }\mathrm{/}\tau$ and independent of $T$ and $\tau$ for $k_{B}T\ll \mathrm{\hslash }\mathrm{/}\tau$. Further the conductivity being independent of $T$ in the ZGS state is examined in terms of Born approximation for the impurity cattering.