Momentum relaxation of holographic Weyl semimetal from massive gravity

We consider the effects of momentum relaxation on the topological quantum phase transitions in holographic Weyl semimetals. The translational symmetry breaking in the field theory is realized in the framework of massive gravity. The quantum phase transition is between a Weyl semimetal phase and a topological trivial phase, which is controlled by M/b, i.e. the ratio of mass parameter and time reversal symmetry breaking parameter. We find that the critical value of the phase transition (M/b)${}_c$, characterized by the anomalous Hall conductivity, decreases with the increasing of graviton mass, i.e. the momentum relaxation strength. There exists a critical value of graviton mass above which the topological phase transition disappears and therefore the Weyl points are destroyed. All these phenomena are qualitatively similar to that of axion fields induced momentum relaxation, indicating that a universal feature emerges in the momentum relaxed holographic Weyl semimetals, which is also consistent with the predictions from weakly coupled field theory.