Superconductivity in transition metal carbides, TaC and HfC: A density functional theory study with local, semilocal, and nonlocal exchange–correlation functionals

We studied electronic, dynamical, and superconducting properties of TaC and HfC using local, semilocal, and nonlocal exchange–correlation functionals in the density functional theory. It turns out that there is a slight shift of Fermi energy and the corresponding density of states with different functionals. However, the phonon frequencies of, especially, the optical modes for both TaC and HfC shift by moderately larger values. The most important differences are observed for the electron–phonon interactions where the electron–phonon coupling constant, λ≈0.9, calculated using the nonlocal correlation functionals, vdW-DF2 and vdW-DF3 for TaC, are in the closest agreement with the experimental results. Although the Kohn anomalies and Fermi surface nesting are critical for the electron–phonon coupling, a significant contribution to λ, for TaC, comes from the regions of the Brillouin zone where the matrix elements have a predominant role. Moreover, the optical modes give 20%–23% of λ for TaC and 50%–57% for HfC.