Effect of Umklapp Scattering on Magnetic Field Penetration Depth in High-T_c Cuprates

抄録

The way how the magnetic field penetration depth (λ) is renormalized by the electron-electron correlation, mainly focused on high-T_c cuprates, is presented. The formula for the current carried by quasiparticle (which plays an essential role on λ^-2 and other transport phenomena) with the Umklapp scattering is derived. By relating the role of the Umklapp scattering with the irreducible four point vertex, how the value of λ^-2 deviates from that of n/m^* (n and m^* are the carrier density and the effective mass, respectively) is investigated. It is analytically shown that this deviation is small in the case where the momentum dependence of the vertex is weak, and is large and negative in the case of the strong antiferromagnetic spin fluctuation. In the latter case it is also derived that the backflow generally takes the opposite sign to the velocity with non-negligible magnitude. The observed doping dependence of λ^-2 in high-T_c cuprates, a peak structure at the slightly overdoped region, is explained by the above analytical consideration and the numerical calculation based on the perturbation theory and the spin fluctuation theory. The consistency between λ^-2 and dλ^-2/dT at absolute zero, which is the problem the isotropic model fails to explain, is also obtained by our theory.