First-principles calculations on the intrinsic resistivity of realistic metals: a case study of monolayer VN.

The Ziman resistivity formula is extensively employed to calculate the intrinsic resistivity of realistic metals using recent works of first-principles calculations. Owing to the approximation, Allen's generalization, which relates the solution of the Boltzmann transport equation (BTE) for metals to the transport electron-phonon (e-ph) spectral function, the applicability of the Ziman resistivity formula still needs to be discussed. In this work, we perform first-principles calculations of the intrinsic resistivity of the VN monolayer, a kind of MXene material, by employing the Ziman resistivity formula and the iterative solution of BTE. We find that in the wide temperature range of 50-1400 K, the intrinsic resistivity of the VN monolayer obtained by means of the two approaches, has the same order of magnitude. However the Ziman resistivity formula fails to correctly describe the Fermi level dependence of the intrinsic resistivity of the VN monolayer. The underlying reason is that the band edge of the VN and hence Van Hove singularity (VHS), is near the shifted Fermi level. We suggest a modified Ziman resistivity formula which is valid even if there is a band edge at the Fermi level.