A general framework for emergent Lorentz violation in Dirac and Weyl semimetals

We use a general framework of Lorentz violation in quantum electrodynamics to study the breaking of emergent Lorentz symmetry in Dirac and Weyl materials. In addition to Weyl semimetals already reported in the literature, we also find Dirac nodal spectra with nodal lines and rings depending on the pattern of Lorentz violation. We further utilize this framework to characterize transport coefficients and report on the electromagnetic response due to all possible effects of Lorentz violation at leading order.