Enhancement of Fermi velocity by electron-electron interactions, and the transport properties of high-T_c superconductors

We consider a composite quasi-2D electron gas, consisting of metallic layers of width d and a background dielectric constant ε{lunate}₁, separated by layers with dielectric constant ε{lunate}₂, where d > a₀, a₀ = h {combining short stroke overlay}² ε{lunate}₁/me² and ε{lunate}₂ ≫ ε{lunate}₁. We show that the Coulomb interaction renormalizes the velocity v(k) for k ≈ k_F, and v(k_F) is increased by a factor close to ε{lunate}₂/ε{lunate}₁. The peak of v(k) around k = k_F is very narrow. Thus the anomalous properties of an electron gas calculated by Lindhard in 1954 for an unscreened electron gas, can persist, under special conditions, even if screening is taken into account. We employ this theory to the normal-state properties of the cuprates. We find that the conductivity is increased by a factor of: [v(k_F)/v⁽⁰⁾(k_F)]² ≈ [ε{lunate}₂/ε{lunate}₁]² due to the velocity renormalization and the resistivity due to elastic scattering becomes temperature-dependent. We account for the conductivity anisotropy, Hall constant, thermoelectric power, and London penetration depth. Measurements of the Fermi velocity by N. Hass, employing Andreev reflection, indicate a significant increase in the velocity close to the Fermi level. This velocity renormalization increases T_c significantly.