Diffusive quantum criticality in three-dimensional disordered Dirac semimetals

Three-dimensional Dirac semimetals are stable against weak potential disorder, but not against strong disorder. In the language of renormalization group, such stability stems from the irrelevance of weak disorder in the vicinity of the noninteracting Gaussian fixed point. However, beyond a threshold, potential disorder can take Dirac semimetals into a compressible diffusive metallic phase through a quantum phase transition (QPT), where density of states at zero energy, quasiparticle lifetime, and metallic conductivity at $T=0$ are finite. Universal behavior of such unconventional QPT is described within the framework of an $\epsilon (=d-2)$ expansion near the lower critical dimension. Various exponents near this quantum critical point are obtained after performing a two-loop perturbative expansion in the vanishing replica limit and we demonstrate that the theory is renormalizable at least to two-loop order. We argue that such QPT is always continuous in nature and shares the same university class with a similar transition driven by odd-parity disorder. The critical exponents are independent of flavor number of Dirac fermions and thus our study can be germane to disordered ${\mathrm{Cd}}_3{\mathrm{As}}_2$ and ${\mathrm{Na}}_3\mathrm{Bi}$. Scaling behaviors of various measurable quantities such as specific heat and density of states across such QPT are proposed.

Figure 1

One-loop (first row) and two-loop diagrams that contribute to the renormalization of the self-energy and disorder vertex in the vanishing replica limit. Solid (dashed) line represents fermions (disorder).