##### Description

__Jose Alarco__

^{1}Peter Talbot

^{1}Ian Mackinnon

^{1}1, Queensland University of Technology, Brisbane, Queensland, Australia

We describe an *ab initio *method to assist prediction of superconductivity in a solid using correlated real and reciprocal space determinants for known or unknown structures. Density functional theory (DFT) calculations for AlB_{2}-type structures, show that the thermal energy (T_{e}) associated with phonon anomalies displays one-to-one correspondence to the experimentally determined superconducting transition temperature (T_{c})^{1}. This correspondence is accurate for a range of conditions^{1-3} including different isotopes, metal substitution (e.g. Al, Ti or Sc) and changes in pressure (-5 GPa to 20 GPa) for MgB_{2}. Similarly, we demonstrate correspondence of T_{e} and T_{c} for other AlB_{2}-type structures^{1} including BaSi_{2} and (Ca_{0.5}Al_{0.5})Si_{2}.

Using DFT, we evaluate electron density differences invoked by atom displacements aligned with phonon modes in MgB_{2} to show that the Fermi energy for the E_{2g} mode alone accounts for the highly covalent B–B bond charge density distribution. Importantly, the band structure becomes tangential to the Fermi level and the Fermi surface undergoes a topological transition at a critical relative displacement of ~ 0.6% from the equilibrium real space position of boron atoms. The difference in Fermi energies at this critical displacement and at the equilibrium position corresponds to the superconducting energy gap. The volume between tubular σ surfaces in reciprocal space controls the depth of the phonon anomaly and is key to understanding superconductivity because it is directly related to the interplay between light and heavy mass σ bands at **G** near the Fermi level.

We extend this *ab initio *method to other superconducting structures including H_{3}S and the hexaborides covering the range of experimental T_{c} values from <10 K to ~200 K for multi-element compounds. Hexaboride structures accommodate a wide range of metals with a corresponding range of electronic properties^{4}. As with MgB_{2} and H_{3}S, the calculated phonon dispersion (PD) for YB_{6} shows a similar proportionate inflexion in the T_{2g} phonon mode for which the T_{e} corresponds with measured T_{c}. These analyses are consistent with “extra” Raman and infra-red (IR) peaks observed in borides^{5,6} that imply lower symmetry superlattices are indicators of superconductivity even in cubic structures. Correlation of Fermi surface transitions with key modes in calculated PDs for variations in temperature, pressure or metal substitution shows that electron density distributions along bonds oriented with phonon mode directions are potential determinants of superconductivity.

1. Alarco, J. A., et al., *Phys. Chem. Chem. P*hys. (2015) 17 (38), 25090.

2. Mackinnon, I. D. R., et al., *Comp. Mater. S*ci. (2017) 130, 191.

3. Alarco, J. A., et al., *Physica C: Supercond. and Appli*cations (2017) 536, 11.

4. Mackinnon, I. D. R., et al., *Mod. & Num. Sim. Mater. Sci*. (2013) 3 (4), 158.

5. Alarco, J. A., et al., *Phys. Chem. Chem. Phys*. (2014) 16, 24443.

6. Bando, H., et al., *J. Phys. Soc. Jpn*. (2011) 80, SA053.