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 QCP 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, share same university class with a similar transition driven by odd-parity disorder, critical exponents are independent of flavor number of Dirac femrions and thus can be germane to disordered Cd$_3$As$_2$, Na$_3$Bi. Scaling behaviors of various measurable quantities, such as specific heat, density of states across such QPT are proposed.