Does $Θ_{II}$-loop-current order coexist with either stripe or checkerboard $d$-wave CDW/PDW order in a hot spot model for cuprate superconductors?

We investigate the dramatic influence of the $\Theta_{II}$-loop-current order on unidirectional and bidirectional $d$-wave CDW/PDW composite orders along axial momenta $(\pm Q_0,0)$ and $(0,\pm Q_0)$ that emerge in an effective hot spot model departing from the three-band Emery model relevant to the phenomenology of the cuprate superconductors. This study is motivated by the compelling evidence that the $\Theta_{II}$-loop-current order described by this model may explain groundbreaking experiments such as Kerr-rotation data and spin-polarized neutron scattering. Here, we demonstrate, within a saddle-point approximation, that the $\Theta_{II}$-loop-current order clearly coexists with bidirectional (i.e. checkerboard) CDW and PDW orders along axial momenta, but is visibly detrimental to the unidirectional (i.e. stripe) case. This result has potentially far-reaching implications for the physics of the cuprates and agrees well with very recent x-ray experiments on YBCO that indicate that at higher dopings the CDW order has indeed a tendency to be bidirectional.