It is well known that at low temperature many metals become superconductors. A metal can be viewed in part as a Fermi liquid of electrons, and below a critical temperature, an attractive phonon-mediated interaction between the electrons near the Fermi surface causes them to pair up and form a condensate of Cooper pairs, which via the Anderson–Higgs mechanism makes the photon massive, leading to characteristic behaviors of a superconductor: infinite conductivity and the exclusion of magnetic fields (Meissner effect). The crucial ingredients for this to occur are:
# a liquid of charged fermions.
# an attractive interaction between the fermions
# low temperature (below the critical temperature)
These ingredients are also present in sufficiently dense quark matter, leading physicists to expect that something similar will happen in that context:
# quarks carry both electric charge and color charge;
# the strong interaction between two quarks is powerfully attractive;
# the critical temperature is expected to be given by the QCD scale, which is of order 100 MeV, or 10 kelvins, the temperature of the universe a few minutes after the Big Bang, so quark matter that we may currently observe in compact stars or other natural settings will be below this temperature.
The fact that a Cooper pair of quarks carries a net color charge, as well as a net electric charge, means that some of the gluons (which mediate the strong interaction just as photons mediate electromagnetism) become massive in a phase with a condensate of quark Cooper pairs, so such a phase is called a "color superconductor". Actually, in many color superconducting phases the photon itself does not become massive, but mixes with one of the gluons to yield a new massless "rotated photon". This is an MeV-scale echo of the mixing of the hypercharge and W bosons that originally yielded the photon at the TeV scale of electroweak symmetry breaking.