Strong correlations between phonon energies and superconducting transition temperatures can be extracted from phonon dispersion calculations using density functional theory for a range of superconducting materials. These correlations are robust and consistent with experimental data for key external conditions including isotope effects, elemental substitutions and pressure variations. Changes in the electronic band structure also correlate with transitions to/from superconductivity but, in general, are less sensitive and less obvious than phonon behaviour. A computational approach that considers both phonons and electrons and the presence or absence of a phonon anomaly works well for conventional superconducting materials with hexagonal, cubic or tetragonal symmetries. Superconductivity in these compounds often involves symmetry reduction in an original non-superconducting parent compound induced, for instance, by substitution or by a dynamic reduction in symmetry shown in electron density distributions and Raman spectra. Such symmetry reduction is effectively modelled with super-lattice constructs which link Raman spectra with key superconducting parameters.
Part of the book: Phonons in Low Dimensional Structures