  Recent measurements of charge instabilities in overdoped compounds rekindled
the proposal that cuprates become superconductors by long-range order through
Josephson coupling between nanoscopic charge domains. We use the theory of
phase-ordering dynamics to show that incommensurate charge density waves (CDWs)
are formed in the CuO planes by a series of free-energy wells separated by
steep barriers. Charge oscillations in these domains give rise to a net
hole-hole attraction proportional to the height of these barriers.
Concomitantly, the self-consistent calculations yield localized superconducting
amplitudes in the CDWdomains characterizing a granular superconductor. We show
that a transition by long-range phase order promoted by Josephson coupling
elucidates many well-known features of cuprates like the high magnetic
penetration depth anisotropy and the origin of the pseudogap, among others.
Furthermore, the average Josephson energy reproduces closely the planar
superfluid density temperature dependence of La-based films and the
superconducting giant proximity effects of cuprates, a 20-year-old open
problem.
