# Pseudo-Fields in Weyl materials

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. We will discuss the effects of inhomogeneities such as lattice deformations or a non-uniform magnetization on the response and the energy spectrum of such materials. These can arise either naturally or by engineering and can result, for example, in a space-dependent Weyl node separation which can be interpreted as an emergent axial vector potential. Consequently, emerging pseudo fields can derive equilibrium bound currents proportional to their strength that average to zero over the sample, and the interplay of pseudo fields and external fields and can redistribute charge or chiral charge in real as well as in momentum space via mechanisms such as the chiral anomaly. In addition, we will discuss how the topological surface states of Weyl semimetals, the Fermi arcs, can be re-interpreted as an n=0 pseudo-Landau level resulting from a pseudo-magnetic field confined to the surface, and how a bulk pseudo-magnetic field creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces. Hallmarks of pseudo-fields can appear in transport, and we discuss ways to detect and quantify them and contrast these with effects arising from external fields. Finally, we will discuss the manifestations of these ideas in metamaterials.