Superconducting correlations induced by charge ordering in cuprate superconductors and Fermi arc formation

We have developed a generalized electronic phase separation model of high-temperature cuprate superconductors that links the two distinct energy scales of the superconducting (SC) and pseudogap (PG) phases via a charge-density-wave (CDW) state. We show that simulated electronic-density modulations resembling the charge order (CO) modulations detected in cuprates intertwine the SC and charge orders by localizing charge and providing the energy scale for a spatially periodic SC attractive potential. Bulk superconductivity is achieved with the inclusion of Josephson coupling between nanoscale domains of intertwined fluctuating CDW and SC orders, and local SC phase fluctuations give rise to the Fermi arcs along the nodal directions of the SC gap. We demonstrate the validity of the model by reproducing the hole-doping dependence of the PG onset temperature $T^*$, and the SC transition temperature $T_c$ of ${\rm YBa_2Cu_3O_y}$ and ${\rm Bi_{2-y}Pb_ySr_{2-z}La_zCuO_{6+\delta}}$. The results show that the periodicity of the CDW order is controlled by the PG energy scale, and the hole-doping dependence of the SC energy gap is controlled by the charge ordering free energy.