Chapters authored
Phonon Dispersions as Indicators of Dynamic Symmetry Reduction in Superconductors
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
Insights from Systematic DFT Calculations on Superconductors
We present three systematic approaches to use of Density Functional Theory (DFT) for interpretation and prediction of superconductivity in new or existing materials. These approaches do not require estimates of free parameters but utilize standard input values that significantly influence computational resolution of reciprocal space Fermi surfaces and that reduce the meV-scale energy variability of calculated values. Systematic calculations on conventional superconductors show that to attain a level of resolution comparable to the energy gap, two key parameters, Δk and the cut-off energy, must be optimized for a specific compound. The optimal level of resolution is achieved with k-grids smaller than the minimum reciprocal space separation between key parallel Fermi surfaces. These approaches enable estimates of superconducting properties including the transition temperature (Tc) via (i) measurement of the equivalent thermal energy of a phonon anomaly (if present), (ii) the distribution of electrons and effect on Fermi energy (EF) when subjected to a deformation potential and (iii) use of parabolic, or higher order quartic, approximations for key electronic bands implicated in electron–phonon interactions. We demonstrate these approaches for the conventional superconductors MgB2, metal substituted MgB2 and boron-doped diamond.
Part of the book: Real Perspective of Fourier Transforms and Current Developments in Superconductivity