Effects of thermal disorder on electronic structure, electron-phonon coupling and spin-fluctuations in high-$T_C$ cuprates

The superconducting $T_C$'s are estimated from the values of electron-phonon and spin-phonon coupling in typical high-$T_C$ cuprates. It is shown that the couplings are peaked for just a few q-vectors because of the 2-dimensional Fermi surface shape. The involvement of few selective spin-phonon modes compensates for the low electronic density-of-states, which allows for a high $T_C$ [1]. Thermal disorder at moderately high temperature perturbs the strongly coupled modes through incoherent potential fluctuations of the Madelung terms, and electronic structure calculations show that the effective spin-phonon coupling suffers from lattice disorder. This effect puts a limit on long-range superconductivity, while fluctuations can persist to higher temperature. BCS-type model calculations are used to show how disorder modifies the superconducting gap and reduces $T_C$. Some ideas of how to recuperate a higher $T_C$ from superconducting fluctuations are discussed. \\[4pt] [1] T. Jarlborg, Solid State Commun. {\bf 181}, 15, (2014).