Chiral anomaly and axial gauge fields in Weyl matter

Oral presentation given at the Conference on Transport at the Nanoscale, held in Cuernavaca (Mexico), on September 25-29th, 2017.After the synthesis of graphene (massless Dirac fermions in 2+1 dimensions) in 2005 a whole new branch of topological materials has emerged which constitute novel physical realizations of high energy systems. Weyl semimetals (WSM) (the 3D graphene) are a material realization of Lorentz violating massless QED in (3+1) dimensions. The recent experimental confirmation has opened a new lab to explore anomaly related phenomena, and a number of experimental observations have already been reported. In graphene, lattice deformations couple to the electronic current in the form of "elastic gauge fields" axial in nature. In this talk we will see that elastic axial gauge fields are also present in the Weyl semimetals. Among the new response functions associated to them, we will show that WSM have an intrinsic Hall viscosity whose coefficient is related to the AAA triangle anomaly. A novel strain-induced chiral magnetic effect will also be present