Conductivity of a Weyl semimetal with donor and acceptor impurities

We study transport in a Weyl semimetal with donor and acceptor impurities. At sufficiently high temperatures transport is dominated by electron-electron interactions, while the low-temperature resistivity comes from the scattering of quasiparticles on screened impurities. Using the diagrammatic technique, we calculate the conductivity $\sigma (T,\omega ,n_A,n_D)$ in the impurities-dominated regime as a function of temperature $T$, frequency $\omega$, and the concentrations $n_A$ and $n_D$ of donors and acceptors and discuss the crossover behaviour between the regimes of low and high temperatures and impurity concentrations. In a sufficiently compensated material [$\mathrm{\mid }{n}_A-n_D\mathrm{\mid }\ll (n_A+n_D)$] with a small effective fine structure constant $\alpha$, $\sigma(\omega,T)\propto T^2/(T^{-2}-i\omega\cdot$\text{const}$)$ in a wide interval of temperatures. For very low temperatures or in the case of an uncompensated material the transport is effectively metallic. We discuss experimental conditions necessary for realising each regime.