A first-principles investigation of structural, dynamical, electronic and phonon-mediated superconducting properties of B3-TMCs (TM=Pd, Pt) using local, semilocal, and nonlocal functionals

The density functional theory was employed to study the structure, electronic bands, phonon spectrum, and electron–phonon interactions in PdC and PtC. The functionals like PW (Perdew-Wang), a local density approximation (LDA), PBE (Perdew–Burke–Ernzerhof), a generalized gradient approximation (GGA), along with the nonlocal functionals, rVV10 and vdW-DF3 that include long range electron–electron correlations in the GGA type functionals, were applied to contrast their performances for the said properties. The absence of negative phonon frequencies predicts the dynamical stability of B3 phase of PdC and PtC. The electronic bands from different methods, if corrected for the constant difference of Fermi energies, show an overwhelming agreement for both materials. Nonetheless, the phonon dispersion curves manifest relatively significant differences in the entire Brillouin Zone. The two materials also manifest low-temperature superconductivity in the B3 phase. The acoustic phonons play a predominant role, up to 88% for PdC and 93% for PtC in electron–phonon coupling. The optical phonons give rise to a minor but appreciable part of $\lambda$, up to 20% for PdC and 24% for PtC. Furthermore, vdW-DF3 leads to a value of $\lambda$ larger than 1.5 and, consequently, the superconducting transition temperature was calculated with the modified Allen–Dynes equation. It turns out that rVV10 gives the closest agreement with the experimental lattice constant for PtC. Furthermore, vdW-DF3, another nonlocal functional, results in a significant enhancement of $\lambda$, and, hence, the superconducting transition temperatures for both the materials.