First-principles study on the electrical resistivity in zirconium dichalcogenides with multi-valley bands: mode-resolved analysis of electron-phonon scattering

Based on the first-principles calculations, we study the electron-phonon scattering effect on the resistivity in the zirconium dichalcogenides, $\text{Zr}_{}\text{S}_{2}$ and $\text{Zr}_{}\text{Se}_{2}$, whose electronic band structures possess multiple valleys at conduction band minimum. The computed resistivity exhibits non-linear temperature dependence, especially for $\text{Zr}_{}\text{S}_{2}$, which is also experimentally observed on some TMDCs such as $\text{Ti}_{}\text{S}_{2}$ and $\text{Zr}_{}\text{Se}_{2}$. By performing the decomposition of the contributions of scattering processes, we find that the intra-valley scattering by acoustic phonons mainly contributes to the resistivity around 50 K. Moreover, the contribution of the intra-valley scattering by optical phonons becomes dominant even above 80 K, which is a sufficiently low temperature compared with their frequencies. By contrast, the effect of the inter-valley scattering is found to be not significant. Our study identifies the characteristic scattering channels in the resistivity of the zirconium dichalcogenides, which provides critical knowledge to microscopically understand electron transport in systems with multi-valley band structure.