  In this study, we have analytically considered a dislocation in
three-dimensional Weyl semimetal and its holographic model. A quantum
singularity that originated in the dislocation creates a defect in momentum
space. This defect causes topologically protected zero-energy mode bound to the
quantum singularity. The defect has two aspects: First, it prevents the
formation of a topological winding number. Second, it provides another
topological number around itself. The gauge field adjusts these effects of the
defect, and it is possible to control the phase transition. Further, from
holographic duality, the quantum singularity is mapped onto a domain wall of
classical gravity. We find that the domain wall causes a violation of gauge
invariance of bulk spacetime. We also demonstrate that the quantum singularity
is comparable to the anomaly from the gauge invariance breaking of the bulk
spacetime, and holographic entanglement entropy reveals the information encoded
in the defect of momentum space.
