Cherenkov radiation in isotropic chiral matter: unlocking threshold-free emission

We investigate Cherenkov radiation in isotropic chiral matter using Carroll-Field-Jackiw electrodynamics, with an axion angle linear in time, to describe a charge moving at constant velocity. By solving the modified Maxwell’s equations in cylindrical coordinates and in the space-frequency domain, we derive closed expressions for the circularly polarized electromagnetic fields contributing independently to the radiation. The dispersion relations are obtained by imposing causality at a cylindrical surface at infinity, ensuring outgoing waves. Contrary to initial suppositions, each spectral energy distribution is gauge-invariant and positive, describing radiation at a characteristic angle. We characterize the angles and identify frequency ranges that allow for zero, one, or two Cherenkov cones. Notably, one sector of the model enables threshold-free Cherenkov radiation from slowly moving charges. Our results agree with partial findings in the nonrelativistic limit of earlier iterative analysis and clarify the regimes in which Cherenkov radiation arises in isotropic chiral matter.

💡 Research Summary

This paper presents a comprehensive theoretical study of Cherenkov radiation (CHR) emitted by a point charge moving at constant velocity through an isotropic chiral medium, using the Carroll‑Field‑Jackiw (CFJ) formulation of electrodynamics. In CFJ theory the axion angle θ(x) is taken to be linear in time, θ = σ t, which introduces a Lorentz‑ and CPT‑violating term proportional to σ c B in Ampère’s law. The resulting modified Maxwell equations contain a “magnetic conductivity” σ that couples directly to the magnetic field, thereby endowing the medium with a chiral anomaly‑driven response distinct from conventional bi‑isotropic chiral media.

The authors first set up the problem with a point charge q traveling along the z‑axis with speed v, and introduce the scalar and vector potentials (Φ, A). By performing a Fourier transform in time they work in the space‑frequency domain (ω) and exploit cylindrical symmetry (ρ, φ, z). Solving the modified Maxwell equations yields two independent circularly polarized eigen‑modes, labelled (+) and (–). Their dispersion relations are  k² = ε ω²/c² ± σ ω/c, showing that the chiral term splits the usual photon branch into two branches with different phase velocities. Imposing causality at an infinitely distant cylindrical surface forces the selection of outgoing waves only, which determines the asymptotic form of the fields.

From the asymptotic fields the authors compute the spectral energy radiated per unit length,  dW/dω = ( q² / π c )