Weyl semimetals and holography

In three spatial dimensions, no fundamental Weyl fermions, i.e. massless fermions, have been found in nature. However, in condensed matter systems, there exist many new kinds of emergent quasiparticles due to the collective behavior of the many body system. One of them is the so-called Weyl (semi-)metal, whose low energy excitations are emergent Weyl fermions. Weyl semimetals are the three dimensional analogue of graphene and have attracted a lot of attention recently. Weyl semimetals have been found in many materials in the laboratory during the last three years. In Weyl semimetals there exists a topological phase transition from the topological nontrivial Weyl semimetal to a topological trivial semimetal or insulator phase. In this talk I will show that using the tools of holography it can be verified that the topological phase transition and the concept of topological semimetal obtained at the weak coupling limit in a Weyl semimetal still exist in the strong coupling limit. The order parameter of the quantum phase transition is the anomalous Hall conductivity. We also show that there is a new prediction for the physics of the quantum critical region of a Weyl semimetal from holography: there exists substantial odd viscosity in the quantum critical region, which is induced by the mixed gauge gravitational anomaly. This is a new observational prediction of the mixed gauge gravitational anomaly, which we hope can be confirmed in experiments.