Quantum Berezinskii-Kosterlitz-Thouless transition in the superconducting phase of (2+1)-dimensional quantum chromodynamics

Abstract

We study superconductivity in the hadron-quark mixed phase of planar quantum chromodynamics (QCD) within the large $N$ limit of a Gross-Neveu model modified by a repulsive vector term. At high densities, the combination of scalar attraction and repulsive space-like part of the vector interaction squeezes quarks into baryonic composite states, i.e., Dirac fermions with even numbers of bosonic vortices attached. The time-like vector component induces Cooper pairing between these Fermi surface modes. Remarkably, at zero temperature, competition between the quark density and mass destroys superconductivity via a Berezinskii-Kosterlitz-Thouless (BKT) phase transition driven by diverging chiral quantum fluctuations near criticality. Dissolution of logarithmically bound singlet diquarks is catalyzed by in-plane chiral mixing associated with $\mathbb{Z}_2 \otimes \mathbb{Z}_2 \to \mathbb{Z}_2$ chiral symmetry breaking of the Fermi surface into a transverse spin-polarized triplet ground state. We calculate the QCD phase diagram for quark chemical potential above the baryon mass based purely on Fermi surface considerations and find good agreement with results obtained by other methods. We address similarities between our quantum BKT transition and those found using holographic techniques.