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For large isospin asymmetries, perturbation theory predicts the QCD groundstate to be a superfluid phase of $u$ and $\bar{d}$ Cooper pairs. This phase,which is denoted as the BCS phase, is expected to be smoothly connected to thestandard phase with Bose-Einstein condensation (BEC) of charged pions at$\mu_I\ge m_\pi/2$ by an analytic crossover. A first hint for the existence ofthe BCS phase, which is likely characterised by the presence of both,deconfinement and charged pion condensation, is coming from the latticeobservation that the deconfinement crossover smoothly penetrates into the BECphase. To further scrutinize the existence of the BCS phase, in thisproceedings article we investigate the complex spectrum of the massive Diracoperator in 2+1-flavor QCD at nonzero temperature and isospin chemicalpotential. The spectral density near the origin is related to the BCS gap via ageneralization of the Banks-Casher relation to the case of complex Diraceigenvalues (derived for the zero-temperature, high-density limits of QCD atnonzero isospin chemical potential).

Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetry