Charge, bond, and pair density wave orders in a strongly correlated system

The coexistence of multiple quasidegenerate orders is the hallmark of the strongly correlated materials. Experiments often reveal several spatially modulated orders in the underdoped cuprates. This has come to the forefront with the possible detection of the pair density wave states. However, microscopic calculations often struggle to stabilize such spatially modulating orders as the ground state in the strong correlation limit. This work uses the t-t′-J model with an additional nearest-neighbor repulsion to stabilize spatially oscillating charge, bond, and pairing orders in the underdoped regime. We employ the standard Gutzwiller approach while treating the inhomogeneity for the spatial orders using the self-consistent Hartree-Fock-Bogoliubov methodology. Our calculations reveal that unidirectional bond density states coexisting with charge and pairing modulations can have lower energy than the uniform superconducting state over an extensive doping range. These modulating states vanish monotonically as the modulation wave vector becomes shorter with increased dopings. The finite momentum orders give way to a vestigial nematic phase on increasing doping which only breaks the rotational symmetry of the system. The nematic order vanishes on further increasing doping, and only uniform superconductivity survives. The spatial features of the ground state at each doping reveal multiple wave vectors, which potentially drive the incommensuration of charge orders. Interestingly, the spatially modulating states are absent when the strong correlations criteria are relaxed, suggesting that the removal of double occupancy aids the stabilization of density wave orders.