Quantum Spin Supersolid as a precursory Dirac Spin Liquid in a Triangular Lattice Cobaltate*

Based on the idea that the Dirac spin liquid is the parent state for numerous competing orders, we propose the triangular lattice antiferromagnet Na2BaCo(PO4)2, which exhibits a quantum spin supersolid, to be a precursory Dirac spin liquid. Despite the presence of a three-sublattice magnetic order resembling a spin ``supersolid'', we suggest that this system is close to a Dirac spin liquid by exploring its spectroscopic response. The physical consequence is examined from the spectroscopic response, and we establish the continuous spectra near the M point in addition to the K point excitation from the spinon continuum on top of the three-sublattice order. This proposal offers a plausible understanding of the recent inelastic neutron scattering measurement in Na2BaCo(PO4)2 and could inspire further research in relevant models and materials.