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We consider the effects of momentum relaxation on the topological quantumphase transitions in holographic Weyl semimetals. The translational symmetrybreaking in the field theory is realized in the framework of massive gravity.We find that the critical value of the phase transition, characterized by theanomalous Hall conductivity, decreases with the increasing of graviton mass,i.e. the momentum relaxation strength. There exists a critical value ofgraviton mass above which the topological phase transition disappears andtherefore the Weyl points are destroyed. All these phenomena are qualitativelysimilar to that of axion fields induced momentum relaxation, indicating that auniversal feature emerges in the momentum relaxed holographic Weyl semimetals,which is also consistent with the predictions from weakly coupled field theory.

Momentum relaxation of holographic Weyl semimetal from massive gravity