Electron-hole liquid model for high-Tc superconductors.

Abstract

We show that the hole concentration dependence of ${T}_{c}$ in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6+\mathrm{x}}$- and ${\mathrm{Nd}}_{1+\mathrm{x}}$${\mathrm{Ba}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathrm{y}}$-type superconductors can be understood within a model electron-boson hole liquid that possesses a linear sound mode like the one in liquid $^{4}\mathrm{He}$. The electronic specific heat follows a ${T}^{3}$ law near T=0. The metal-insulator transition found in these compounds is proposed to be connected with the vanishing of the sound velocity at small carrier densities.