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We study the quantum phase diagram of a three dimensional non-interactingDirac semimetal in the presence of either quenched axial or scalar potentialdisorder, by calculating the average and the typical density of states as wellas the inverse participation ratio using numerically exact methods. We showthat as a function of the disorder strength a half-filled (i.e. undoped) Diracsemimetal displays three distinct ground states, namely an incompressiblesemimetal, a compressible diffusive metal, and a localized Anderson insulator,in stark contrast to a conventional dirty metal that only supports the lattertwo phases. We establish the existence of two distinct quantum critical points,which respectively govern the semimetal-metal and the metal-insulator quantumphase transitions and also reveal their underlying multifractal nature. Awayfrom half-filling the (doped) system behaves as a diffusive metal that canundergo Anderson localization only, which is shown by determining the mobilityedge and the phase diagram in terms of energy and disorder.

Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals