Quantum spin supersolid as a precursory Dirac spin liquid in a triangular lattice antiferromagnet

Based on the recent experiments on the triangular lattice antiferromagnet Na 2 BaCo(PO 4 ) 2 , we propose the easy-axis XXZ spin-1 / 2 model on the triangular lattice, that exhibits a quantum spin supersolid, to be a precursory Dirac spin liquid. Despite the presence of a three-sublattice magnetic order as 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. Moreover, the satellite peaks were predicted at the mid-points connecting the I' and K points. This proposal offers a plausible understanding of the recent inelastic neutron scattering measurement in Na 2 BaCo(PO 4 ) 2 and could inspire further research in relevant models and materials, such as K 2 Co(SeO 3 ) 2 and Rb 2 Co(SeO 3 ) 2 , and even more anisotropic magnets like PrMgAl 11 O 19 .