Magnetoresistance in High-TcSuperconductors: The Role of Vertex Corrections

Abstract

In high- T c cuprates, the orbital magnetoresistance in plane ( Δ ρ/ρ) 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 Δ ρ/ρ and the Hall coefficient ( R H ), Δρ/ρ∝( R H /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 expression for Δ ρ/ρ by including the vertex corrections (VC's) to keep the conservation laws, and find the approximate relation Δ ρ/ρ∝ξ AF 4 ρ -2 · H 2 (ξ AF being the AF correlation length) in the presence of AF fluctuations. The factor ξ AF 4 , which comes from the VC's for the current, gives the additional temperature dependence. By taking account of the relation R H ∝ξ AF 2 [Kontani et al. : Phys. Rev. B 59 (1999) 14723], we can naturally explain the modified Kohler's rule. In conclusion, based on the Fermi liquid theory, the famous seemingly non-Fermi liquid behaviors of R H and Δ ρ/ρ in high- T c cuprates are naturally understood on an equal footing.