Chiral crystal in cold QCD matter at intermediate densities?

The analogue of Overhauser (particle-hole) pairing in electronic systems (spin-density waves with non-zero total momentum $Q)$ is analyzed in finite-density QCD for 3 colors and 2 flavors, and compared to the color-superconducting BCS ground state (particle-particle pairing, $Q=0).\mathrm{}$ The calculations are based on effective nonperturbative four-fermion interactions acting in both the scalar diquark as well as the scalar-isoscalar quark-hole (“σ”) channel. Within the Nambu-Gorkov formalism we set up the coupled channel problem, including multiple chiral density wave formation, and evaluate the resulting gaps and free energies. Employing medium-modified instanton-induced ’t Hooft interactions, as applicable around ${\mu }_q\simeq 0.4\mathrm{GeV}$ (or 4 times nuclear saturation density), we find the “chiral crystal phase” to be competitive with the color superconductor.