  The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has
Weyl nodes in bulk excitations and Fermi arcs surface states. We study the
effects of disorder and localization in WSMs and find three exotic phase
transitions. (I) Two Weyl nodes near the Brillouin zone boundary can be
annihilated pairwise by disorder scattering, resulting in the opening of a
topologically nontrivial gap and a transition from a WSM to a three-dimensional
(3D) quantum anomalous Hall state. (II) When the two Weyl nodes are well
separated in momentum space, the emergent bulk extended states can give rise to
a direct transition from a WSM to a 3D diffusive anomalous Hall metal. (III)
Two Weyl nodes can emerge near the zone center when an insulating gap closes
with increasing disorder, enabling a direct transition from a normal band
insulator to a WSM. We determine the phase diagram by numerically computing the
localization length and the Hall conductivity, and propose that the exotic
phase transitions can be realized on a photonic lattice.

Mesoscale and Nanoscale Physics