Bond-length fluctuations in the copper oxide superconductors

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 CuO 2 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.