Nonsaturating linear resistivity up to 900 K in ${\text{MgB}}_2$

In this work, we report resistivity measurements on ${\text{MgB}}_2$ polycrystalline samples with increasing degree of doping (disorder) up to temperatures higher than 900 K. In all cases the normal state curves are linear with increasing temperatures, with no sign of flattening or downward bending (saturation) at high temperature. This behavior, in sharp contrast to what is observed in superconducting compounds such as A15 and Chevrel phases, can be explained considering the dominant $\pi$ contribution to the electric conduction, together with the smaller electron-phonon coupling of $\pi$ carriers in ${\text{MgB}}_2$, as compared to characteristic coupling strength of those compounds. This indicates that in ${\text{MgB}}_2$ the disorder introduced in the lattice by thermal oscillations even at 900 K can still be considered as a perturbation within the Boltzmann description of transport.

Figure 1

(Color online) Upper panel: Rescaled resistivity curves of Al-doped samples up to 910 K. Lower panel: same resistivity curves, after subtraction of the respective residual resistivity values, plotted in log-log scale. The dashed lines indicate $T^3$ and $T$ slopes.

Figure 2

(Color online) Rescaled resistivity curves of the undoped ${\text{MgB}}_2$ sample S0 (upper panel) and most doped ${\text{Mg}}_{0.6}{\text{Al}}_{0.4}{\text{B}}_2$ sample S3 (lower panel) together with the fitting curves obtained (i) with ${\rho }_{\text{ideal}}$ given by the B-G Eq. (1) and ${\rho }_{\text{sat}}$ obtained from the Gunnarsson-Calandra Eq. (3), assuming four intermixed bands (green continuous lines, not distinguishable from experimental data points in this scale, in both panels) and (ii) with ${\rho }_{\text{ideal}}$ given again by the B-G Eq. (1) and ${\rho }_{\text{sat}}$ obtained from Ioffe-Regel formula (2) assuming $\pi$ and $\sigma$ bands in parallel (red dashed lines, clearly distinguishable from experimental data points at the highest temperatures in the upper panel).