Impact of crystal structure on electron-phonon coupling and phonon-mediated properties, The

Abstract

The impact of crystal structure on electron-phonon coupling (EPC) was analyzed by computing (i) the electron-phonon mediated superconductivity and (ii) electron-phonon induced eigenenergy renormalizations. Our primary goal is to compare these EPC effects in a wide range of materials with various crystal symmetries and compositions in order to re- veal the connection between EPC and crystal structure. First-principles calculations were done employing the density functional theory (DFT) and the density functional perturbation theory (DFPT) within the linear-response approach, for obtaining electron-phonon matrix elements, which were then used in post-processing codes to calculate superconductivity and electronic structure renormalization. The Migdal-Eliashberg formalism and the McMillan equations were used to determine the electron-phonon coupling strength (λ) and the critical temperature (Tc) for sodium (Na) under high pressures. A thorough investigation was performed of superconductivity in Na from ambient pressure to 260 GPa, where the metal-to-insulator transition occurs, and at 15.5 terapascals (TPa), after Na reenters a metallic phase. We evaluated phonon dispersions and the superconducting parameters for body-centered cubic (bcc), fcc, cI16, tI19, and cI24 Na. Our results for the bcc and fcc phases are consistent with prior theory, and the previously unknown critical temperatures and electron-phonon coupling strengths were calculated for the cI16, tI19, and cI24 phases. The peak value of λ, between 0 and 30 TPa, was calculated to be 0.5 for cI16-Na. However, as superconductivity is associated with λ ≥ 1, we conclude that Na is not likely to present scientifically interesting superconductivity, even at ultra-high pressures, despite favorable comparisons to structurally similar superconducting alkali metals. The second EPC-induced phenomenon we examined is the electronic structure renormalization. Calculations and careful convergence tests were carried out for two silicon (Si) allotropes, three carbon (C) allotropes, and four boron nitride (BN) polymorphs. Determination of the energy shifts from the DFPT electron-phonon matrix elements was done within the Allen-Heine-Cardona (AHC) theory in the adiabatic approximation as well as with non-adiabatic corrections. Our results demonstrate that the magnitude of the renormalizations at T = 0 K, or zero-point renormalization (ZPR), of the electronic band structure is comparable to the many-body GW corrections to Kohn-Sham eigenenergies for some materials, and, thus, need to be considered in electronic structure calculations. Examination of the phonon dispersion for each structure along with the non-adiabatic ZPR magnitudes revealed that bulk materials with optical phonons at higher maximum frequencies, have larger ZPR magnitudes, and that two dimensional structures exhibit significantly different behavior than those of the bulk materials. This study investigates two well-known phonon-mediated properties: superconductivity and eigenenergy renormalization. These results are not only useful in these two fields. As the core part of these investigations is the computation of the electron-phonon coupling elements, they are also pertinent to the study optical and transport properties affected or mediated by lattice vibrations.