Characterizing the Larkin-Ovchinnikov-Fulde-Ferrel phase induced by the chromomagnetic instability

Abstract

We discuss possible destinations from the chromomagnetic instability in color superconductors with Fermi surface mismatch $\ensuremath{\delta}\ensuremath{\mu}$. In the two-flavor superconducting (2SC) phase we calculate the effective potential for color vector potentials ${\mathbit{A}}_{\ensuremath{\alpha}}$ which are interpreted as the net momenta $\mathbit{q}$ of pairing in the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) phase. When $1/\sqrt{2}<\ensuremath{\delta}\ensuremath{\mu}/\ensuremath{\Delta}<1$ where $\ensuremath{\Delta}$ is the gap energy, the effective potential suggests that the instability leads to a LOFF-like state which is characterized by color-rotated phase oscillations with small $\mathbit{q}$. In the vicinity of $\ensuremath{\delta}\ensuremath{\mu}/\ensuremath{\Delta}=1/\sqrt{2}$ the magnitude of $\mathbit{q}$ continuously increases from zero as the effective potential has negative larger curvature at vanishing ${\mathbit{A}}_{\ensuremath{\alpha}}$ that is the Meissner mass squared. In the gapless 2SC (g2SC) phase, in contrast, the effective potential has a minimum at $g{\mathbit{A}}_{\ensuremath{\alpha}}\ensuremath{\sim}\ensuremath{\delta}\ensuremath{\mu}\ensuremath{\sim}\ensuremath{\Delta}$ even when the negative Meissner mass squared is infinitesimally small. Our results imply that the chromomagnetic instability found in the gapless phase drives the system toward the LOFF state with $\mathbit{q}\ensuremath{\sim}\ensuremath{\delta}\ensuremath{\mu}$.