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We investigate the influence of rotation on the dynamical chiral symmetrybreaking in strongly interacting matter. We develop a self-consistentBogoliubov-de Gennes-like theoretical framework to study the inhomogeneouschiral condensate and the possible chiral vortex state in rotating finite-sizematter in four-fermion interacting theories. We show that for sufficientlyrapid rotation in $2+1$ dimensions, the ground state can be a chiral vortexstate, a type of topological defect in analogy to superfluids andsuperconductors. The vortex state exhibits pion condensation, providing a newmechanism to realize pseudoscalar condensation in strongly interacting matter.

Chiral vortices and pseudoscalar condensation due to rotation