  Exotic physics often emerges around quantum criticality in metallic systems.
Here we explore the nature of topological phase transitions between 3D
double-Weyl semimetals and insulators (through annihilating double-Weyl nodes
with opposite chiralities) in the presence of Coulomb interactions. From
renormalization-group (RG) analysis, we find a non-Fermi-liquid quantum
critical point (QCP) between the double-Weyl semimetals and insulators when
artificially neglecting short-range interactions. However, it is shown that
this non-Fermi-liquid QCP is actually unstable against nematic ordering when
short-range interactions are correctly included in the RG analysis. In other
words, the putative QCP between the semimetals and insulators is preempted by
emergence of nematic phases when Coulomb interactions are present. We further
discuss possible experimental relevance of the nematicity-preempted QCP to
double-Weyl candidate materials HgCr2Se4 and SrSi2.
