  Dynamic charge transfers, or charge fluxes, generated by anharmonic phonon
couplings have previously shown some fundamental connections with the pseudogap
phase and other important phases in cuprate superconductors. The anharmonicity
here suggests the importance of nonadiabatic behaviors of charge fluxes in
cuprates. These charge fluxes will result in the dynamic charge transfer that
can be directly calculated by the charge difference induced by phonons in
density functional theory simulations. However, retrieving the flux field from
the calculated charge transfer is nontrivial. In this article, a new method is
developed to solve these fluxes, which help identify anharmonically coupled
phonons as the generator of nonlocal flux flows beyond local oscillations in
cuprates, especially at high frequencies. A strength metric of such nonlocal
fluxes shows a strong correlation to the maximum superconducting transition
temperature T_(c,max) of different cuprate families. A unique picture is thus
proposed where heavy fluxes tunnel through a dynamic energy band near the Fermi
level, providing the attraction force through a Bernoulli-like mechanism for
the formation of Cooper pairs. Adding the dynamic band to our band simulation
also reproduces the flat band feature that appears below the superconducting
transition temperature Tc in previous experimental measurements.
