Disorder-driven transition in Dirac semimetals and semiconductors

Motivated by Weyl semimetals and weakly doped semiconductors, I will discuss recent work on non-Anderson disorder-driven criticality in weakly doped semimetals and semiconductors. I will show that above a critical dimensions at low-electron density these systems generically exhibit a novel disorder-driven quantum phase transition that manifests itself in the critical behavior of the single particle density of states, electrical transport, wavefunction multi-fractality and other observables. These can be computed via a controlled renormalization-group analysis.