Antagonistic impact of thermal expansion and phonon anharmonicity on the phonon-limited resistivity of elemental metals from first principles

Abstract

Understanding electrical resistivity in metals remains a central challenge in quantifying charge transport at finite temperature. Current first-principles calculations based on the Boltzmann transport equation often match experiments, yet they almost always neglect the effect of thermal expansion and phonon anharmonicity. We show that both effects exert an opposite impact on electron-phonon coupling and on electrical resistivity. Thermal expansion enhances the coupling and leads to overestimation of resistivity, whereas anharmonic effects reduce it. By explicitly incorporating both effects, we establish a more complete description of resistivity in elemental metals, demonstrated here for Pb, Nb, and Al.

Figures (4)

• Figure 1: Electrical resistivity of Pb from 10 to 610 K using the iterative Boltzmann transport equation (IBTE). The green and blue markers are computed without and with thermal expansion (TE), without considering the phonon anharmonicity, while the computation of pink and orange markers takes the phonon anharmonicity into account. The experimental data are from Ref. hellwege1982.
• Figure 2: Phonon dispersion of Pb including (a) lattice thermal expansion (TE) effect where calculations are harmonic with a temperature-dependent lattice parameters, (b) without TE and with temperature-dependent phonon anharmonicity, and (c) with TE and phonon anharmonicity. In all cases the gray line is the harmonic phonon dispersion computed with density functional perturbation theory (DFPT) without TE. (d) Phonon dispersion of Pb calculated with TE and phonon anharmonicity at 110 K compared with experimental data at 100 K measured by neutron scattering from Ref. Brockhouse1962 ($\times$ markers) and from Ref. Brockhouse1961 (open and closed circles).
• Figure 3: Electron scattering rates $\tau_{n\mathbf{k}}^{-1}$ of Pb at $\pm$ 0.3 eV around the Fermi energy $\varepsilon^{\rm F}$ at (a) 310 K and (b) 610 K. (c) Spectral decomposition of the electron scattering rates averaged around the fermi energy as a function of phonon frequency at 610 K. In each subfigures, we show results without thermal expansion (TE) and without phonon anharmoncity (blue), with TE and without anharmonicity (orange), and with TE and anharmoncity (green).
• Figure 4: Electrical resistivity of Al from 0 to 1000 K and Nb from 0 to 3000 K using the iterative Boltzmann transport equation (IBTE). The green and blue markers are computed without and with thermal expansion (TE), without considering the phonon anharmonicity, while the computation of orange markers takes the phonon anharmonicity into account. The experimental data are from Ref. hellwege1982.