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Motivated by Weyl semimetals and weakly doped semiconductors, we studytransport in a weakly disordered semiconductor with a power-law quasiparticledispersion $\xi_{\bf k}\propto k^\alpha$. We show, that in $2\alpha$ dimensionsshort-correlated disorder experiences logarithmic renormalisation from allenergies in the band. We study the case of a general dimension $d$ using arenormalisation group, controlled by an $\varepsilon=2\alpha-d$-expansion.Above the critical dimensions, conduction exhibits alocalisation-delocalisation phase transition or a sharp crossover (depending onthe symmetries of the Hamiltonian) as a function of disorder strength. Weutilise this analysis to compute the low-temperature conductivity in Weylsemimetals and weakly doped semiconductors near and below the critical disorderpoint.

Critical transport in weakly disordered semiconductors and semimetals