Magnetoresistance in High-Tc Superconductors: The Role of Vertex Corrections

In high-Tc cuprates, the orbital magnetoresistance in plane (MR, $\Delta\rho/\rho$) is anomalously enhanced at lower tempemeratures compared with conventional Fermi liquids, and thus Kohler's rule is strongly violated. Moreover, it should be noted that an intimate relation between the MR and the Hall coefficient ($R_H$), $\Delta\rho/\rho \propto (R_H/\rho)^2$, holds well experimentally, and is called the "modified Kohler's rule". In this letter, we study this long-standing problem in terms of the nearly antiferromagnetic (AF) Fermi liquid. We analyze the exact expression for the MR by including the vertex corrections (VC's) to keep the conservation laws, and find the approximate "scaling relation" $\Delta\rho/\rho \propto \xi_{AF}^4 /\rho^2$ ($\xi_{AF}$ being the AF correlation length.) in the presence of AF fluctuations. The factor $\xi_{AF}^4$, which comes from the VC's for the current, gives the additional temperature dependence. By taking account of the relation $R_H \propto \xi_{AF}^2$ [Kontani et al., PRB 59 (1999) 14723.], we can naturally explain the modified Kohler's rule. In conclusion, based on the Fermi liquid theory, the famous {\it seemingly} non-Fermi liquid behaviors of the Hall coefficient and the MR in high-Tc cuprates are naturally understood on an equal footing.