Fermi surface nesting and intrinsic resistivity of beryllium: First-principles calculations

Within the semiclassical Boltzmann transport theory, we perform a systematic first-principles calculation of the intrinsic resistivity of beryllium, a nodal-line semimetal. The Wannier interpolation technique to treat the electron-phonon ($e$-ph) interaction is employed to guarantee a high precision of the numerical results. Our numerical results of the intrinsic resistivity of beryllium agree quantitatively with experimental data in a large temperature range. We find that around each joint region between the electron and hole pockets, the Fermi surface of beryllium forms a pair of vertical facets (parallel to $c$ axis). Then, the nesting effect between such Fermi surface segments near inequivalent vertices of the hexagonal Brillouin zone can be realized by $e$-ph scattering with a relatively short phonon wavelength. Such a Fermi surface nesting effect plays the dominant role in the intrinsic resistivity. It is also the underlying mechanism for linear temperature dependence of the intrinsic resistivity from a very low critical temperature (200 K). In contrast, the contribution of the topological nontrivial states near the nodal line to the intrinsic resistivity is less important because only a few of such states appear in the vicinity of the Fermi surface due to the sizable dispersion of the nodal line.