  Taking into account the interplay between the disorder and Coulomb
interaction, the phase diagram of three-dimensional anisotropic Weyl semimetal
is studied by renormalization group theory. Weak disorder is irrelevant in
anisotropic Weyl semimetal, while the disorder becomes relevant and drives a
quantum phase transition from semimetal to compressible diffusive metal phases
if the disorder strength is larger than a critical value. The long-range
Coulomb interaction is irrelevant in clean anisotropic Weyl semimetal. However,
interestingly, we find that the long-range Coulomb interaction exerts a
dramatic influence on the critical disorder strength for phase transition to
compressible diffusive metal. Specifically, the critical disorder strength can
receive a prominent change even though an arbitrarily weak Coulomb interaction
is included. This novel behavior is closely related to the anisotropic
screening effect of Coulomb interaction,and essentially results from the
specifical energy dispersion of the fermion excitations in anisotropic Weyl
semimetal. The theoretical results are helpful for understanding the physical
properties of the candidates of anisotropic Weyl semimetal, such as pressured
BiTeI, and some other related materials.
