Theoretical seminar | 10 May 2023

Carroll, Field and Jackiw (CFJ) proposed a modified theory of electrodynamics to demonstrate the existence of Lorentz invariance violations in fundamental interactions. Remarkably, this theory describes the effective electromagnetic response of Weyl semimetals (chiral matter) [1,2]. In condensed matter the Lorentz violating coefficients accounts for the separation in energy and momentum space of the Weyl nodes. CFJ-electrodynamics is a particular case of axion electrodynamics, which has previously been shown to produce reversed Cherenkov radiation in topological insulators [3]. The induced axion field in Weyl semimetals arises due to the chiral anomaly. Here we present a study on the modifications of the electromagnetic radiation in the CFJ-model [4]. By employing the stationary phase approximation we construct the Green's matrix in the radiation zone which allows the calculation of the corresponding electromagnetic potentials and fields for arbitrary sources. We obtain a general expression for the angular distribution of the radiated energy per unit frequency. As an application, we consider a fast charge moving at constant velocity inside an ideal Weyl semimetal, where we find the emergence of zero, one or two Cherenkov cones depending on the velocity of the particle and the medium's refractive index. Each cone corresponds to the two polarizations of the light due to the birefringence in the medium, which can allow the experimental detection of this effect.

Main paper/arXiv, related to the seminar, and other references

[1] S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990).
[2] A. A. Zyuzin and A. A. Burkov, Phys. Rev. B 86, 115133 (2012).
[3] O. J. Franca, L. F. Urrutia, and O. Rodríguez-Tzompantzi, Phys. Rev. D 99, 116020 (2019).
[4] E. Barredo and L. F. Urrutia, “Cherenkov radiation in chiral media,” (2022), arXiv:2207.01104 [hep-ph].