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Register a new userOrigin of the high-energy kink or the waterfall effect in the photoemission spectrum of the ${rm Bi_2Sr_2CaCu_2O_8}$ high-temperature superconductor
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The high-energy kink or the waterfall effect seen in the photoemission spectra of the cuprates is suggestive of the coupling of the quasiparticles to a high energy bosonic mode with implications for the mechanism of superconductivity. Recent experiments however indicate that this effect may be an artifact produced entirely by the matrix element effects, i.e. by the way the photoemitted electron couples to the incident photons in the emission process. In order to address this issue directly, we have carried out realistic computations of the photo-intensity in ${rm Bi_2Sr_2CaCu_2O_8}$ (Bi2212) where the effects of the matrix element are included together with those of the corrections to the self-energy resulting from electronic excitations. Our results demonstrate that while the photoemission matrix element plays an important role in shaping the spectra, the waterfall effect is a clear signature of the presence of strong coupling of quasiparticles to electronic excitations.
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The condensation energy can be shown to be a moment of the change in the occupied part of the spectral function when going from the normal to the superconducting state. As a consequence, there is a one to one correspondence between the energy gain associated with forming the superconducting ground state, and the dramatic changes seen in angle resolved photoemission spectra. Some implications this observation has are offered.
Ultrahigh resolution angle-resolved photoemission spectroscopy with low-energy photons is used to study the detailed momentum dependence of the well-known nodal kink dispersion anomaly of Bi2Sr2CaCu2O8+{delta}. We find that the kinks location transitions smoothly from a maximum binding energy of about 65 meV at the node of the d-wave superconducting gap to 55 meV roughly one-third of the way to the antinode. Meanwhile, the self-energy spectrum corresponding to the kink dramatically sharpens and intensifies beyond a critical point in momentum space. We discuss the possible bosonic spectrum in energy and momentum space that can couple to the k-space dispersion of the electronic kinks.
The Ferrell-Glover-Tinkham (FGT) sum rule has been applied to the temperature dependence of the in-plane optical conductivity of optimally-doped YBa_2Cu_3O_{6.95} and underdoped YBa_2Cu_3O_{6.60}. Within the accuracy of the experiment, the sum rule is obeyed in both materials. However, the energy scale omega_c required to recover the full strength of the superfluid rho_s in the two materials is dramatically different; omega_c simeq 800 cm^{-1} in the optimally doped system (close to twice the maximum of the superconducting gap, 2Delta_0), but omega_c gtrsim 5000 cm^{-1} in the underdoped system. In both materials, the normal-state scattering rate close to the critical temperature is small, Gamma < 2Delta_0, so that the materials are not in the dirty limit and the relevant energy scale for rho_s in a BCS material should be twice the energy gap. The FGT sum rule in the optimally-doped material suggests that the majority of the spectral weight of the condensate comes from energies below 2Delta_0, which is consistent with a BCS material in which the condensate originates from a Fermi liquid normal state. In the underdoped material the larger energy scale may be a result of the non-Fermi liquid nature of the normal state. The dramatically different energy scales suggest that the nature of the normal state creates specific conditions for observing the different aspects of what is presumably a central mechanism for superconductivity in these materials.
Super-high resolution laser-based angle-resolved photoemission measurements have been performed on a high temperature superconductor Bi_2Sr_2CaCu_2O_8. The band back-bending characteristic of the Bogoliubov-like quasiparticle dispersion is clearly revealed at low temperature in the superconducting state. This makes it possible for the first time to experimentally extract the complex electron self-energy and the complex gap function in the superconducting state. The resultant electron self-energy and gap function exhibit features at ~54 meV and ~40 meV, in addition to the superconducting gap-induced structure at lower binding energy and a broad featureless structure at higher binding energy. These information will provide key insight and constraints on the origin of electron pairing in high temperature superconductors.
In conventional metals, electron-phonon coupling, or the phonon-mediated interaction between electrons, has long been known to be the pairing interaction responsible for the superconductivity. The strength of this interaction essentially determines the superconducting transition temperature TC. One manifestation of electron-phonon coupling is a mass renormalization of the electronic dispersion at the energy scale associated with the phonons. This renormalization is directly observable in photoemission experiments. In contrast, there remains little consensus on the pairing mechanism in cuprate high temperature superconductors. The recent observation of similar renormalization effects in cuprates has raised the hope that the mechanism of high temperature superconductivity may finally be resolved. The focus has been on the low energy renormalization and associated kink in the dispersion at around 50 meV. However at that energy scale, there are multiple candidates including phonon branches, structure in the spin-fluctuation spectrum, and the superconducting gap itself, making the unique identification of the excitation responsible for the kink difficult. Here we show that the low-energy renormalization at ~50 meV is only a small component of the total renormalization, the majority of which occurs at an order of magnitude higher energy (~350 meV). This high energy kink poses a new challenge for the physics of the cuprates. Its role in superconductivity and relation to the low-energy kink remains to be determined.
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