Coexistence ofΘII-loop-current order with checkerboardd-wave CDW/PDW order in a hot-spot model for cuprate superconductors

We investigate the strong influence of the ${\mathrm{\ensuremath{\Theta}}}_II$-loop-current order on both unidirectional and bidirectional $d$-wave charge-density-wave/pair-density-wave (CDW/PDW) composite orders along axial momenta $(\ifmmode\pm\else\textpm\fi{}{Q}₀,0)$ and $(0,\ifmmode\pm\else\textpm\fi{}{Q}₀)$ 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 ${\mathrm{\ensuremath{\Theta}}}_II$-loop-current order described by this model may explain groundbreaking experiments such as spin-polarized neutron scattering performed in these materials. Here, we demonstrate, within a saddle-point approximation, that the ${\mathrm{\ensuremath{\Theta}}}_II$-loop-current order clearly coexists with bidirectional (i.e., checkerboard) $d$-wave 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.