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

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In high-Tc cuprates, the orbital magnetoresistance in plane (Δρ/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 Δρ/ρ and the Hall coefficient (RH), 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 expression for Δρ/ρ by including the vertex corrections (VC's) to keep the conservation laws, and find the approximate relation Δρ/ρ ∝ ξAF4 ρ-2 · H2 (ξAF being the AF correlation length) in the presence of AF fluctuations. The factor ξAF4, which comes from the VC's for the current, gives the additional temperature dependence. By taking account of the relation RH ∝ ξAF2 [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 RH and Δρ/ρ in high-Tc cuprates are naturally understood on an equal footing.
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