# Reversed electromagnetic Vavilov-\v{C}erenkov radiation in naturally existing magnetoelectric media

## TL;DR

This paper theoretically demonstrates the possibility of reversed Vavilov-Cerenkov radiation in naturally occurring magnetoelectric media, especially topological insulators, by analyzing electromagnetic responses at interfaces and particle motion.

## Contribution

It introduces a Green's function approach for magnetoelectric interfaces and predicts reversed Cerenkov radiation in natural materials like topological insulators.

## Key findings

- Reversed Vavilov-Cerenkov radiation can occur in magnetoelectric media.
- Estimated frequencies of reversed radiation are comparable to experimental values in metamaterials.
- Green's function method can be generalized to various geometries.

## Abstract

We consider two semi-infinite magnetoelecteric 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 which can be directly generalized to cylindrical and spherical configurations of two magnetoelectrics separated by an interface. We establish the far-field approximation of the 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-\v{C}erenkov radiation in naturally existing magnetoelectric media. In the case where one of the magnetolectrics is a 3D topological insulator, ${\rm TlBiSe}_2$ for example, located in front of a regular insulator, we estimate that an average forward Vavilov-\v{C}erenkov radiation with frequency $\sim 2.5 \,\, {\rm eV}$ ($\sim 500\,\, {\rm nm}$) will produce a highly suppressed reversed Vavilov-\v{C}erenkov radiation which can be characterized by an effective frequency in the range of $\sim (4\times 10^{-3}-0.5) \,\, {\rm meV}$. However, this value compares favorably with recent measurements in left-handed metamaterials yielding reversed Vavilov-\v{C}erenkov radiation with frequencies of the order of $(1.2-3.9)\times 10^{-2}\,\, {\rm meV}$.