Linear temperature dependence of intrinsic resistivity of metals determined by electronic structure

Abstract

The temperature dependence of the intrinsic resistivity ($\rho$) limited by electron-phonon scattering is a significant physical property of metals. When the temperature ($T$) is sufficiently high, the $\rho$-$T$ relationship becomes linear for all metallic materials. According to conventional Bloch-Gr{\"u}neisen theory, the characteristic temperatures for the onset of linear $\rho$-$T$ relationship are defined by Debye temperature ($T_D$) or Bloch-Gr{\"u}neisen temperature ($T_{BG}$), both of which are tightly associated with the phonon dispersion. In the present work, we propose a novel characteristic temperature ($T_e$) to govern the linear $\rho$-$T$ relationship that arises from the electronic structure, unrelated to the phonon dispersion. By performing the first-principles calculations, we demonstrate that the rhombohedral trilayer graphene can exemplify such an electronic structure determined linear $\rho$-$T$ relationship. We expect that, in additional to other characteristic temperatures, such as $T_D$ and $T_{BG}$, the effect of $T_e$ should be considered when analysing the temperature dependence of the intrinsic resistivity of materials with band singularities, such as the flat bands or band edges, occurring close to Fermi level.