  We investigate color superconducting phases of cold quark matter at densities
relevant for the interiors of compact stars. At these densities, electrically
neutral and weak-equilibrated quark matter can have unequal numbers of up,
down, and strange quarks. The QCD interaction favors Cooper pairs that are
antisymmetric in color and in flavor, and a crystalline color superconducting
phase can occur which accommodates pairing between flavors with unequal number
densities. In the crystalline color superconductor, quarks of different flavor
form Cooper pairs with nonzero total momentum, yielding a condensate that
varies in space like a sum of plane waves. Rotational and translational
symmetry are spontaneously broken. We use a Ginzburg-Landau method to evaluate
candidate crystal structures and predict that the favored structure is
face-centered-cubic. We predict a robust crystalline phase with gaps comparable
in magnitude to those of the color-flavor-locked phase that occurs when the
flavor number densities are equal. Crystalline color superconductivity will be
a generic feature of the QCD phase diagram, occurring wherever quark matter
that is not color-flavor locked is to be found. If a very large flavor
asymmetry forbids even the crystalline state, single-flavor pairing will occur;
we investigate this and other spin-one color superconductors in a survey of
generic color, flavor, and spin pairing channels. Our predictions for the
crystalline phase may be tested in an ultracold gas of fermionic atoms, where a
similar crystalline superfluid state can occur. If a layer of crystalline quark
matter occurs inside of a compact star, it could pin rotational vortices,
leading to observable pulsar glitches.
