Unconventional superconductivity as a quantum Kuramoto synchronization problem in random elasto-nuclear oscillator networks

We formulate the problem of unconventional d − wave superconductivity, with phase fluctuations, pseudogap phenomenon, and local Cooper pairs, in terms of a synchronization problem in random, quantum dissipative, elasto-nuclear oscillator networks. The nodes of the network correspond to localized, collective quadrupolar vibrations of nuclei-like, elastic inhomogeneities embedded in a dissipative medium. Electrons interacting with such vibrations form local Cooper pairs, with a superfluid d − wave pseudogap Δ PG , due to an effective, short range attractive interaction of d x 2 − y 2 character. Phase coherent, bulk superconductivity, with a d − wave gap Δ, is stabilized when the oscillator network is asymptotically entangled in a nearly decoherence-free environment. Phase coherence will in turn be destroyed, at T c , when the thermal noise becomes comparable to the coupling between oscillators, the superfluid density K . The 2Δ/ k B T c ratio is a function of Kuramoto’s order parameter, r = 1 − K c / K , for the loss of synchronization at K c , and is much larger than the nonuniversal 2Δ PG / k B T * ratio, where T * is the temperature at which Δ PG is completely destroyed by thermal fluctuations. We discuss our findings in connection to the available data for various unconventionally high-temperature superconductors.