Consequences of a condensed matter realization of Lorentz-violating QED in Weyl semi-metals

In Lorentz violating quantum electrodynamics (QED) it is known that a radiatively induced Chern-Simons term appears in the effective action for the gauge field, which is finite but undetermined. This ambiguity is shown to be absent in a condensed matter realization of such a theory in Weyl semi-metals due to the existence of a full microscopic model from which this effective theory emerges. Physically observable consequences such as birefringence are also discussed in this scenario.

Figure 1

Illustrative picture of a system that realizes the Weyl semi-metal phase at low energies: a periodic array of alternating normal (N) and topological insulators (TIs) [19]. The various parameters of the model are shown schematically: ${\Delta }_s$ is the hopping of an electron to a different surface within the same layer, ${\Delta }_D$ controls the hopping of an electron to a different layer, $d$ is the spacing between topological insulator layers and the symbol $i$ labels the layers.