Reversed electromagnetic Vavilov-Čerenkov radiation in naturally existing magnetoelectric media

We consider two semi-infinite magnetoelectric media separated by a planar interface whose electromagnetic response is described by axion electrodynamics. The time-dependent Green's function characterizing this geometry is obtained by a method that can be directly generalized to cylindrical and spherical configurations of two magnetoelectrics separated by an interface. We establish the far-field approximation of Green's function and apply these results to the case of a charged particle moving from one medium to the other at a high constant velocity perpendicular to the interface. From the resulting angular distribution of the radiated energy per unit frequency, we provide theoretical evidence for the emergence of reversed Vavilov-Čerenkov radiation in naturally existing magnetoelectric media. In the case where one of the magnetoelectrics is a 3D topological insulator, TlBiSe₂, for example, located in front of a regular insulator, we estimate that an average forward Vavilov-Čerenkov radiation with frequency ∼2.5 eV (∼500 nm ) will produce a highly suppressed reversed Vavilov-Čerenkov radiation, which can be characterized by an effective frequency in the range of ∼(4 ×10^-3-0.5 ) meV . However, this value compares favorably with recent measurements in left-handed metamaterials yielding reversed Vavilov-Čerenkov radiation with frequencies of the order of (1.2 - 3.9 )×10^-2 meV .