A mechanism for Fermi-surface-topology tuned superconductivity in the cuprates

Based on recent magnetic-quantum-oscillation, ARPES, neutron-scattering and other data, we propose that superconductivity in the cuprates occurs via a convenient matching of the spatial distribution of incommensurate spin fluctuations to the amplitude and phase of the $d_{x^2-y^2}$ Cooper-pair wavefunction; this establishes a robust causal relationship between the lengthscale of the fluctuations and the superconducting coherence length. It is suggested that the spin fluctuations are driven by the Fermi surface, which is prone to nesting; they couple to the itinerant holes via the on-site Coulomb correlation energy, which inhibits double occupancy of spins or holes. The maximum energy of the fluctuations gives an appropriate energy scale for the superconducting $T_{\rm c}$. Based on this model, one can specify the design of solids that will exhibit ``high $T_{\rm c}$'' superconductivity.