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

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