Cherenkov Radiation and Non-Dielectric Materials

[Drakkith]

Cherenkov radiation is described as being generated by a charged particle moving through a dielectric medium with a velocity greater than c/n, where n is the refractive index in that medium. Since n varies with frequency, there is a cutoff where n drops below 1 and no radiation is emitted above that frequency (except due to some special mechanisms that I don't want to get into).

My question is what happens if a charged particle moves at relativistic velocities through a non-dielectric medium, such as a metal or semiconductor material? Do these materials even have a refractive index?

 

[DrDu]

Also metals and semiconductors are dielectrics, however with a complex dielectric constant. The imaginary part of the dielectric constant being linked to conductivity. An approximation for the dielectric constant of metals is the so-called Lindhard dielectric function:
https://en.wikipedia.org/wiki/Lindhard_theory