Local dynamical lattice instabilities: Prerequisites for resonant pairing superconductivity

Fluctuating local diamagnetic pairs of electrons, embedded in a Fermi sea, are candidates for non-phonon-mediated superconductors without the stringent conditions on ${T}_{c}$ which arise in phonon-mediated BCS classical low-${T}_{c}$ superconductors. The local accumulations of charge, from which such diamagnetic fluctuations originate, are irrevocably coupled to local dynamical lattice instabilities and form composite charge-lattice excitations of the system. For a superconducting phase to be realized, such excitations must be itinerant spatially phase-coherent modes. This can be achieved by resonant pair tunneling in and out of polaronic cation-ligand sites. Materials in which superconductivity driven by such local lattice instability can be expected have a ${T}_{c}$ which is controlled by the phase stiffness rather than the amplitude of the diamagnetic pair fluctuations. Above ${T}_{c}$, a pseudogap phase will be maintained up to ${T}^{\ensuremath{\ast}}$, at which this pairing amplitude disappears. We discuss the characteristic local charge and lattice properties which characterize this pseudogap phase and which form the prerequisites for establishing a phase-coherent macroscopic superconducting state.