Color superconductivity


Color superconductivity is a phenomenon predicted to occur in quark matter if the baryon density is sufficiently high and the temperature is not too high. Color superconducting phases are to be contrasted with the normal phase of quark matter, which is just a weakly interacting Fermi liquid of quarks.
In theoretical terms, a color superconducting phase is a state in which the quarks near the Fermi surface become correlated in Cooper pairs, which condense. In phenomenological terms, a color superconducting phase breaks some of the symmetries of the underlying theory, and has a very different spectrum of excitations and very different transport properties from the normal phase.

Description

Analogy with superconducting metals

It is well known that at low temperature many metals become superconductors. A metal can be viewed 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 the characteristic behaviors of a superconductor; infinite conductivity and the exclusion of magnetic fields. The crucial ingredients for this to occur are:
  1. a liquid of charged fermions.
  2. an attractive interaction between the fermions
  3. low temperature
These ingredients are also present in sufficiently dense quark matter, leading physicists to expect that something similar will happen in that context:
  1. quarks carry both electric charge and color charge;
  2. the strong interaction between two quarks is powerfully attractive;
  3. the critical temperature is expected to be given by the QCD scale, which is of order 100 MeV, or 1012 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 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 W3 bosons that originally yielded the photon at the TeV scale of electroweak symmetry breaking.

Diversity of color superconducting phases

Unlike an electrical superconductor, color-superconducting quark matter comes in many varieties, each of which is a separate phase of matter. This is because quarks, unlike electrons, come in many species. There are three different colors and in the core of a compact star we expect three different flavors, making nine species in all. Thus in forming the Cooper pairs there is a 9×9 color-flavor matrix of possible pairing patterns. The differences between these patterns are very physically significant: different patterns break different symmetries of the underlying theory, leading to different excitation spectra and different transport properties.
It is very hard to predict which pairing patterns will be favored in nature. In principle this question could be decided by a QCD calculation, since QCD is the theory that fully describes the strong interaction. In the limit of infinite density, where the strong interaction becomes weak because of asymptotic freedom, controlled calculations can be performed, and it is known that the favored phase in three-flavor quark matter is the color-flavor-locked phase. But at the densities that exist in nature these calculations are unreliable, and the only known alternative is the brute-force computational approach of lattice QCD, which unfortunately has a technical difficulty that renders it useless for calculations at high quark density and low temperature.
Physicists are currently pursuing the following lines of research on color superconductivity:
The only known place in the universe where the baryon density might possibly be high enough to produce quark matter, and the temperature is low enough for color superconductivity to occur, is the core of a compact star. There are many open questions here: