We study the stability of three-dimensional incompressible Weyl semimetals in the presence of random quenched charge impurities. Combining numerical analysis and scaling theory, we show that, in the presence of sufficiently weak randomness, (i) the Weyl semimetal remains stable, while (ii) the double-Weyl semimetal gives rise to compressible diffusive metal where the mean density of states at zero energy is finite. At stronger disorder, the Weyl semimetal undergoes a quantum phase transition and enter into a metallic phase. The mean density of states at zero energy serves as the order parameter and displays single-parameter scaling across such a disorder driven quantum phase transition. We numerically determine various exponents at the critical point, which appear to be insensitive to the number of Weyl pairs. We also extract the extent of the quantum critical regime in disordered Weyl semimetals and the phase diagram of dirty double-Weyl semimetals at finite energies.

• Received 3 August 2015
• Revised 25 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.201302