Velocity renormalization near the Mott transition in a perfectly ordered lattice (II)

We consider a medium-density electron gas, near the Wigner-Mott transition, immersed in a medium with a background dielectric constant ε₀(q, ω)that is very large at q = 0, ω = 0, but falls sharply with increasing q and/or ω. We consider the dependence of the screening parameter for state k on the energy of this state. We find that the electronic velocity is enhanced considerably at k = k_F, somewhat similar to the enhancement found by Lindhard in 1954 for an unscreened electron gas. We use parameters applicable to high-T_c cuprates. We find that the maximum of v(k) around k_F is very sharp, the width being a few meV, somewhat smaller than the frequency at which the dielectric constant ε₀(q, ω) drops. We relate this velocity peak to the normal-state transport properties of the cuprates and several other systems, and to the superconductivity. We point out specific experiments that suggest a large enhancement ofv_F.