Pseudo-electromagnetic fields in 3D topological semimetals

Dirac and Weyl semimetals react to position-dependent and time-dependent perturbations, such as strain, as if subject to emergent electromagnetic fields, known as pseudo-fields. Pseudo-fields differ from external electromagnetic fields in their symmetries and phenomenology and enable a simple and unified description of a variety of inhomogeneous systems. We review the different physical means of generating pseudo-fields, the observable consequences of pseudo-fields and their similarities to and differences from electromagnetic fields. Among these differences is their effect on quantum anomalies - absences of classical symmetries in the quantum theory - which we revisit from a quantum field theory and a semi-classical viewpoint. We conclude with predicted observable signatures of the pseudo-fields and the status of the nascent experimental research. Pseudo-electromagnetic fields emerge in inhomogeneous materials. This Review discusses the properties of such fields in the context of 3D topological semimetals, the origin and consequences of pseudo-fields in real materials and their field theory description. Key pointsPseudo-electromagnetic fields arise in inhomogeneous Weyl and Dirac semimetals.The action of a pseudo-magnetic field within a Weyl node is indistinguishable from the action of an external magnetic field.Pseudo-magnetic fields generate Landau levels and activate the chiral anomaly for Weyl semimetals.Pseudo-electric fields lead to chiral charge redistribution and ultrasound attenuation.Pseudo-fields have been observed in metamaterials.