The crystallography of strange quark matter

Abstract

Cold three-flavour quark matter at large (but not asymptotically large) densities may exist as a crystalline colour superconductor. We explore this possibility by calculating the gap parameter Δ and free energy Ω(Δ) for possible crystal structures within a Ginzburg–Landau approximation, evaluating Ω(Δ) to order Δ6. We develop a qualitative understanding of what makes a crystal structure stable and find two structures with particularly large values of Δ and the condensation energy, within a factor of 2 of those for the CFL phase known to characterize QCD at asymptotically large densities. The robustness of these phases results in their being favoured over wide ranges of density and though it also implies that the Ginzburg–Landau approximation is not quantitatively reliable, previous work suggests that it can be trusted for qualitative comparisons between crystal structures. We close with a look ahead at the calculations that remain to be done in order to make contact with observed pulsar glitches and neutron star cooling.