Resistivity Exponents in 3D Dirac Semimetals From Electron-Electron Interaction

We study the resistivity of three-dimensional semimetals with linear dispersion in the presence of on-site electron-electron interaction. The well-known quadratic temperature dependence of the resistivity of conventional metals is turned into an unusual $T^6$ behavior. An analogous change affects the thermal transport, preserving the linearity in $T$ of the ratio between thermal and electrical conductivities. These results hold from weak coupling up to the nonperturbative region of the Mott transition. Our findings yield a natural explanation for the hitherto not understood large exponents characterizing the temperature dependence of transport experiments on various topological semimetals.

Figure 1

(a) Dirac or Weyl dispersion (for $k_z=0$) and DOS with cutoff $\mathrm{\Lambda }$ in $k$ space and energy half-bandwidth, indicated by $D$. (c) Temperature exponents for scattering rate and resistivity with Hubbard repulsion $U$, sketched in (b), comparing 3D Dirac or Weyl semimetals against conventional Fermi liquids.

Figure 2

(a) DMFT results for the resistivity $\rho$ of a 3D Dirac or Weyl semimetal at zero doping, as a function of the temperature $T$ for different values of the interaction strength $U/D$ (color bar), in units of ${\rho }_0=6{\pi }^2{\hslash }^{3}v/(e^{2}D)$. The dashed lines indicate the asymptotic behavior for low temperature and weak coupling and for large temperature, respectively. (b) DMFT phase diagram, where the color indicates $\partial \log \rho /\partial \log T$, i.e., the exponent of the $T$ dependence of $\rho$.

Figure 3

DMFT results for the resistivity as a function of temperature of a Dirac semimetal for different fillings at interaction strength $U=2D$. The inset shows experimental data for ${\mathrm{Cd}}_3{\mathrm{As}}_2$ from Ref. [41].