Phonon Dispersions as Indicators of Dynamic Symmetry Reduction in Superconductors

Abstract

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.

Insights from Systematic DFT Calculations on Superconductors

“…Thus, parallel or nearly parallel FSs attributable to the superconducting condition [44], no longer exist with a 0.6% shift in atom position(s) [28]. A shift of atom position(s) is also reflected in the form and energy of key phonon modes in the corresponding PD for MgB 2 [26]. An atom displacement of 0.6% along B-B for MgB 2 is not unreasonable at temperatures >40 K [28].…”

“…In this regard, MgB 2 offers good opportunity to evaluate this potential due to well defined crystallography and the key role ascribed to σ bands and superconductivity [12,34]. DFT calculations for a compositional suite, or structure type, produce EBSs that show, in general, similar formats even when two different functional approximations are used [26]. A typical outcome for MgB 2 using the LDA approximation in the CASTEP module of Materials Studio using a k-grid value of 0.008 Å −1 is shown in Figure 1.…”

“…This circumstance occurs for MgB 2 in which one of the dominant E 2g phonon modes -shown to be intimately involved in electron-phonon coupling at the onset of superconductivity [17,34] -aligns with B-B bonds in the ab plane [36]. Using DFT, we can model the effect of bond deformation along specific planar orientations by displacing atoms from their structural equilibrium positions consistent with the direction of the E 2g phonons [26,28]. Under different extents of displacement, electron density distributions along the B-B bond and the corresponding EBS, can be determined [28,36].…”

“…Enlarged view of EBS around Γ for MgB 2 using LDA functional and Δk = 0.018 Å −1 showing (a) degenerate σ bands at equilibrium (blue lines) and (b) after atom displacement D x = 0.063 Å (red lines) along the E 2g mode direction; note the split of σ bands causing loss of degeneracy which coincides with loss of superconductivity [26].…”

“…In other work, we extended this systematic approach to evaluate PDs and EBSs for a wide range of metal diboride compounds (e.g. ScB 2 , YB 2 , TiB 2 ) using DFT at appropriate computational resolution [26].…”