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 AlB2-type structures, show that the thermal energy (Te) associated with phonon anomalies displays one-to-one correspondence to the experimentally determined superconducting transition temperature (Tc)1. This correspondence is accurate for a range of conditions1-3 including different isotopes, metal substitution (e.g. Al, Ti or Sc) and changes in pressure (-5 GPa to 20 GPa) for MgB2. Similarly, we demonstrate correspondence of Te and Tc for other AlB2-type structures1 including BaSi2 and (Ca0.5Al0.5)Si2.
Using DFT, we evaluate electron density differences invoked by atom displacements aligned with phonon modes in MgB2 to show that the Fermi energy for the E2g 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 H3S and the hexaborides covering the range of experimental Tc 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 properties4. As with MgB2 and H3S, the calculated phonon dispersion (PD) for YB6 shows a similar proportionate inflexion in the T2g phonon mode for which the Te corresponds with measured Tc. These analyses are consistent with “extra” Raman and infra-red (IR) peaks observed in borides5,6 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. Phys. (2015) 17 (38), 25090.
2. Mackinnon, I. D. R., et al., Comp. Mater. Sci. (2017) 130, 191.
3. Alarco, J. A., et al., Physica C: Supercond. and Applications (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.