Two-component superconductivity. I. Introduction and phenomenology

A two-component theory of superconductivity is developed where one electronic component provides mobility and the other provides pairing. For the Cu-O-based high-${\mathrm{T}}_{\mathrm{c}}$ materials the two components are identified with mobile electronic states associated Cu-O planes, and localized negative-U states associated with oxygen vacancies in the Cu-O planes. An explicit comparison of phenomenology with BCS theory is performed including comparison with experiments on ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. The discussion includes quantitative comparison of the superconducting properties ${\mathrm{T}}_{\mathrm{c}}$, Δ, ${\mathrm{H}}_{\mathrm{c}}$, and ξ. Long-wave collective excitations, normal-state properties including resistance and tunneling, and the isotope shift are described. Unusual properties are predicted including neutral-fermion excitations, a spreading of the fermionic gap onset, a separation between the resistive transition ${\mathrm{T}}_{\mathrm{c}}^{\prime }$ and the evaporation of the condensate ${\mathrm{T}}_{\mathrm{c}}$, anomalies in sound and bulk modulii at ${\mathrm{T}}_{\mathrm{c}}$, linear temperature dependence of normal-state resistivity, linear voltage dependence in normal-state tunneling conductance, and finite zero-bias conductance in superconducting-state tunneling. A new signature of structural coherence obtained by channeling experiments is indicated.