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The Chiral Magnetic Effect (CME) has been investigated as a new transportphenomenon in condensed matter. Such an effect appears in systems with chiralfermions and involves an electric current generated by a magnetic field bymeans of an "exotic" magnetic conductivity. This effect can also be connectedwith extensions of the usual Ohm's law either in magnetohydrodynamics or inLorentz-violating scenarios. In this work, we study the classical propagationof electromagnetic waves in isotropic dispersive matter subject to ageneralized Ohm's law. The latter involves currents linear in the magneticfield and implies scenarios inducing parity violation. We pay special attentionto the case of a vanishing electric conductivity. For a diagonal magneticconductivity, which includes the CME, the refractive index is modified suchthat it implies birefringence. For a nondiagonal magnetic conductivity,modified refractive indices exhibiting imaginary parts occur ascribing aconducting behavior to a usual dielectric medium. Our findings provide newinsight into typical material properties associated with a magneticconductivity.

Magnetic-conductivity effects on electromagnetic propagation in dispersive matter