Temperature-dependent electron-phonon spectral function and the intrinsic resistivity of a metal: A case study of monolayer Ti2N

The transport spectral function of electron-phonon ($e$-ph) interaction in the double $\ensuremath{\delta}$-function approximation (DDFA) is extensively employed to calculate the intrinsic resistivity (arising from $e$-ph scattering) of metallic materials in recent works of first-principles calculations. In contrast, a more fundamental transport spectral function with the Fermi smearing effect due to finite temperature ($T$) and nonzero phonon frequency is less involved. In this work, we perform first-principles calculations of the intrinsic resistivity of ${\mathrm{Ti}}₂\mathrm{N}$ monolayer, a potential MXene material, by employing the two kinds of spectral function. We find that the spectral function with the DDFA fails to describe correctly the temperature dependence of the intrinsic resistivity of ${\mathrm{Ti}}₂\mathrm{N}$ monolayer at $T>250$ K, much lower than the Debye temperature. The underlying reason is that ${\mathrm{Ti}}₂\mathrm{N}$ monolayer has a multisheet Fermi surface formed by several bands, and some band edges are very close to the Fermi surface. Our results suggest that the transport spectral function with the Fermi smearing effect, instead of the one with the DDFA, is always adequate for studying the intrinsic resistivity of realistic materials on the level of first-principles calculations. In addition, we give a brief remark on the intrinsic resistivity of ${\mathrm{Ti}}₂\mathrm{N}$ monolayer, in contrast with other typical two-dimensional materials, which is significant from the viewpoint of application of such an MXene material.