Theory of magnetoresistance in correlated electron systems: modified Kohler rule in high-Tc superconductors

Abstract

We present a theoretical study for the violation of Kohler's rule in high-Tc cuprates, where both the Hall coefficient (RH) and the orbital magnetoresistance in plane (Δρ/ρ) are anomalously enhanced at lower temperatures. Moreover, an intimate relation among them, Δρ/ρ∝(RH/ρ)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 expressions for RH and Δρ/ρ by including the vertex corrections (VCs) to keep the conservation laws, and find the approximate relations RH∝ξAF2 and Δρ/ρ∝ξAF4·ρ−2·H2, respectively. (ξAF is the AF correlation length.) Thus, the strong temperature dependence of ξAF in the presence of AF fluctuations violates Kohler's rule, whereas the modified Kohler's rule holds well according to our study. In conclusion, the famous seemingly non-Fermi liquid behaviors of magnetotransport phenomena in high-Tc cuprates are naturally understood based on the Fermi liquid theory.