Energy-dependent scaling of incoherent spectral weight and the origin of the waterfalls in high-Tc cuprates

The exotic physics in condensed matter systems, such as high-Tc superconductivity in cuprates, is due to the properties of the elementary excitations and their interactions. The dispersion of the electronic states revealed by angle-resolved photoemission spectroscopy (ARPES) provides a chance to understand these excitations. Recently, a "high energy anomaly" or "waterfall-like" feature in cuprates' dispersion has been reported and studied theoretically. Most of the current views argue that it is the result of some many-body effect at a specific high energy scale (e.g. ~ 0.3eV), though there are other arguments that this is an artificial effect. Here, we report a systematic ARPES study on the "high energy anomaly" in Bi2212 samples over multiple Brillouin zones and with a large variety of ARPES matrix elements. We find that the incoherent weight of the electron spectral function at high binding energy is intimately linked to the energy of the dispersive coherent weight through an unexpected but simple relationship with no special energy scales. This behavior in concert with strong k-dependent matrix element effects gives rise to the heavily studied "waterfall" behavior.