  The double Weyl semimetal (DWSM) is a newly proposed topological material
that hosts Weyl points with chiral charge n=2. The disorder effect in DWSM is
investigated by adopting the tight-binding Hamiltonian. Using the transfer
matrix method and the noncommutative Kubo formula, we numerically calculate the
localization length and the Hall conductivity in the presence of the on-site
nonmagnetic disorder or orbital (spin-flip) disorders, and give the
corresponding global phase diagrams. For the on-site nonmagnetic disorder, the
system undergoes the DWSM-3D quantum anomalous hall (3D QAH) and normal
insulator (NI)-DWSM phase transitions, and evolves into the diffusive metal
(DM) phase before being localized by strong disorders, which is consistent with
the Weyl semimetal. For \sigma_x orbital disorder, we find that increasing
disorder can generate a pair of Weyl nodes at the boundary of the Brillouin
zone and induce a 3D QAH-DWSM phase transition. Then we investigate the
combined effect of orbital disorders for both disordered 3D QAH phase and DWSM
phase. The disorder-induced transitions can be well understood in terms of an
effective medium theory based on self-consistent Born approximation.
