Chiral pair density wave as the precursor of pseudogap in kagom\'e superconductors

Motivated by scanning tunnelling microscopy experiments on AV$_3$Sb$_5$ (A = Cs, Rb, K) that revealed periodic real-space modulation of electronic states at low energies, I show using model calculations that a tripple-$\bf Q$ chiral pair density wave (CPDW) is generated in the superconducting state by a charge order of $2a\! \times \!2a$ superlattice periodicity, intertwined with a time-reversal symmetry breaking orbital loop current. The CPDW correlation survives even when the long-range superconducting phase coherence is diminished by a magnetic field or temperature. The superconducting critical field is enhanced beyond the Chandrasekhar-Clogston limit, pointing to a rare quantum state above the superconducting transition. The presented results suggest that the CPDW can be regarded as the origin of the pseudogap observed near the superconducting transition.