LAUSR

For copper-based superconductors, the maximum superconducting transition temperature T_{c,max} of different families measured from experiment can vary from 38 K in La_{2}CuO_{4} to 135 K in HgBa_{2}Ca_{2}Cu_{3}O_{8} at the optimal hole doping concentration. We demonstrate herein, using ab initio computations, a new trend suggesting that the cuprates with stronger out-of-CuO_{2}-plane chemical bonding between the apical anion (O, Cl) and apical cation (e.g., La, Hg, Bi, Tl) are generally correlated with higher T_{c,max} in experiments. We then show the underlying fundamental phenomena of coupled apical charge flux and lattice dynamics when the apical oxygen oscillates vertically. This triggers the charge flux among the apical cation, apical anion, and the in-plane CuO_{4} unit. The effect not only dynamically modulates the site energy of the hole at a given Cu site to control the in-plane charge transfer energy, but also can modulate the in-plane hole hopping integral simultaneously in a dynamic way by the cooperative apical charge fluxes.