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We study the stability of three-dimensional incompressible Weyl semimetals inthe presence of random quenched charge impurities. Combining numerical analysisand scaling theory we show that in the presence of sufficiently weak randomness(i) Weyl semimetal remains stable, while (ii) double-Weyl semimetal gives riseto compressible diffusive metal where the mean density of states at zero energyis finite. At stronger disorder, Weyl semimetal undergoes a quantum phasetransition and enter into a metallic phase. Mean density of states at zeroenergy serves as the order parameter and displays single-parameter scalingacross such disorder driven quantum phase transition. We numerically determinevarious exponents at the critical point, which appear to be insensitive to thenumber of Weyl pairs. We also extract the extent of the quantum critical regimein disordered Weyl semimetal and the phase diagram of dirty double Weylsemimetal at finite energies.

Dirty Weyl semimetals: Stability, phase transition and quantum criticality