Inhomogeneous Weyl Semimetals

Topological Weyl semimetals have an energy spectrum that hosts non-degenerate Weyl nodes appearing in pairs of opposite chirality, with a finite separation in momentum space that protects them. Inhomogeneities such as lattice deformations or a non-uniform magnetization couple to the electronic degrees of freedom and can affect their response and energy spectrum. These can arise either naturally or by engineering and can result, for example, in a space-dependent nodal separation which can be interpreted as an emergent axial vector potential. As we show, the resulting pseudo-fields represent a powerful concept with several profound consequences, such as equilibrium bound currents, and unconventional anomaly terms that allow for pumping and redistribution of charge or chiral charge in real as well as in momentum space.
Moreover, it is directly linked and allows for a reinterpretation of the physics of Fermi arcs. Hallmarks of pseudo-fields can appear in transport, and we discuss ways to detect and quantify them and contrast our findings with effects arising from external fields.