Vavilov-Cherenkov radiation for parallel motion in three-dimensional topological insulators

TL;DR

This paper investigates how Vavilov-Cherenkov radiation is modified when a charged particle moves parallel to an interface between topological insulators and magnetoelectric media, revealing asymmetric radiation patterns and enhanced retarding forces.

Contribution

It provides analytical expressions for electromagnetic fields and radiation patterns near topological insulator interfaces, highlighting topological effects on Cherenkov radiation.

Findings

Radiation along the Cherenkov cone is inhomogeneous and asymmetric.

Enhanced retarding force in the ultrarelativistic regime.

Analytical expressions derived for specific topological insulators.

Abstract

Our study delves into the modifications observed in Vavilov-Cherenkov radiation when its generating charged particle moves parallel to an interface formed by two generic magnetoelectric media, focusing on topological insulators. We compute the electromagnetic field through the Green's function. Applying the far-field approximation and the steepest descent method, we derive analytical expressions for the electric field, revealing contributions from spherical and lateral waves with topological origins. Subsequently, we analyze the angular distribution of the radiation, particularly focusing on parallel motions in close proximity to the interface. Our findings indicate that the radiation along the Vavilov-Cherenkov cone is inhomogeneous and asymmetric. We analyze the radiated energy at both sides of the interface. Finally, we discuss the particle's retarding force, which is notably enhanced in the ultrarelativistic regime. We illustrate these results for the topological insulator TlBiSe$_2$ and the magnetoelectric TbPO$_4$.