When low- and high-energy electronic responses meet in cuprate superconductors

The existence of coherent quasiparticles near the Fermi energy in the low temperature state of high-temperature superconductors has been well established by angle-resolved photoemission spectroscopy (ARPES). This technique directly probes the momentum-resolved electronic excitation spectrum of the CuO$_2$ planes. We present a study of close to optimally doped La$_{1.83}$Sr$_{0.17}$CuO$_4$ in the superconducting state and report an abrupt change in the quasiparticle spectral function, as we follow the dispersion of the ARPES signal from the Fermi energy up to 0.6 eV. The interruption in the quasiparticle dispersion separates coherent quasiparticle peaks at low energies from broad incoherent excitations at high energies. We find that the boundary between these low-energy and high-energy features exhibits a cosine-shaped momentum dependence, reminiscent of the superconducting d-wave gap. Further intriguing similarities between characteristics of the incoherent excitations and quasiparticle properties (lifetime, Fermi arcs) suggest a close relation between the electronic response at high and low energies in cuprate superconductors.