Theory of the Hall coefficient and resistivity for the layered organic superconductorsκ−(BEDT−TTF)2X

In the organic superconducting $\kappa -(\mathrm{BEDT}-\mathrm{TTF}{)}_{2}X$ compounds, various transport phenomena exhibit striking non-Fermi liquid behaviors, which should be the important clues to understanding the electronic state of this system. Especially, the Hall coefficient ${(R}_{\mathrm{H}})$ shows Curie-Weiss-type temperature dependence, which is similar to that of high-$T_{\mathrm{c}}$ cuprates. In this paper, we study a Hubbard model on an anisotropic triangular lattice at half filling, which is an effective model of $\kappa -(\mathrm{BEDT}-\mathrm{TTF}{)}_{2}X$ compounds. Based on the fluctuation-exchange approximation, we calculate the resistivity $\left(\rho \right)$ and $R_{\mathrm{H}}$ by taking account of the vertex corrections for the current, which is necessary for satisfying the conservation laws. Our theoretical results $R_{\mathrm{H}}\propto T^{-1}$ and $\cot {\theta }_{\mathrm{H}}\propto T^2$ explain the experimental behaviors well, which are unable to be reproduced by the conventional Boltzmann transport approximation. Moreover, we extend the standard Eliashberg’s transport theory and derive the more precise formula for the conductivity, which becomes important at higher temperatures.