Superconductivity in the copper oxides occurs at a crossover from localized to
itinerant electronic behaviour, a transition that is first order. A spinodal phase
segregation is normally accomplished by atomic diffusion; but where it
occurs at too low a temperature for atomic diffusion, it may be realized
by cooperative atomic displacements. Locally cooperative, fluctuating
atomic displacements may stabilize a distinguishable phase lying between a
localized-electron phase and a Fermi-liquid phase; this intermediate phase exhibits
quantum-critical-point behaviour with strong electron–lattice interactions making
charge transport vibronic. Ordering of the bond-length fluctuations at lower
temperatures would normally stabilize a charge-density wave (CDW),
which suppresses superconductivity. It is argued that in the copper oxide
superconductors, crossover occurs at an optimal doping concentration for
the formation of ordered two-electron/two-hole bosonic bags of spin S = 0 in a
matrix of localized spins; the correlation bags contain two holes in a linear cluster
of four copper centres ordered within alternate Cu–O–Cu rows of a CuO2
sheet. This ordering is optimal at a hole concentration per Cu atom of p ≈ 1/6,
but it is not static. Hybridization of the vibronic electrons with the phonons that
define long-range order of the fluctuating (Cu–O) bond lengths creates barely
itinerant, vibronic quasiparticles of heavy mass. The heavy itinerant vibrons form
Cooper pairs having a coherence length of the dimension of the bosonic bags.
It is the hybridization of electrons and phonons that, it is suggested,
stabilizes the superconductive state relative to a CDW state.