Is there a theoretical minimum to the Phase velocity of light?

So diamond has the highest refractive index and presumably the phase velocity of light is reduced by a factor (about 2.4) of the refractive index of diamond.

Is there a theoretical minimum that a media can slow down light (phase velocity ) whether visible light or any other EM ?

Stated another way, Can some material exist in the universe that has a refractive index of 10 or 100 or 1000 … for any of the wavelengths of the EM spectrum ?

Diamond is pretty high, as ordinary materials go (though I think there are a few others that are higher). But there are some weird materials that manage indices of refraction up around 10^8. There’s probably no fundamental limit.

Weird as in highly complex molecule manufactured in a lab, or weird as in Dwarf star alloy?

Weird as in made in a lab, though I don’t recall any details of how they do it.

Dwarf-star materials also tend to be very weird, but usually in the opposite direction, with all other speeds being much higher (like a speed of sound a third as large as the speed of light).

There are ways to reduce the group velocity of light far below c in a material. One experiment slowed it down to 17 meters per second. I’m not sure if that’s what you’re thinking of. But, as I understand it, the group velocity is not the same as the phase velocity.