Characteristics of oxygen isotope substitutions in the quasiparticle spectrum of Bi ₂ Sr ₂ CaCu ₂ O _8+δ

Abstract

Abstract. -There is an ongoing debate about the nature of the bosonic excitations responsible for the quasiparticle self energy in high temperature superconductors -are they phonons or spin fluctuations? We present a careful analysis of the bosonic excitations as revealed by the 'kink' feature at 70 meV in angle resolved photoemission data using Eliashberg theory for a d-wave superconductor. Starting from the assumption that nodal quasiparticles are not coupled to the (π, π) magnetic resonance, the sharp structure at 70 meV can be assigned to phonons. We find that not only can we account for the shifts of the kink energy seen on oxygen isotope substitution but also get a quantitative estimate of the fraction of the area under the electron-boson spectral density which is due to phonons. We conclude that for optimally doped Bi2Sr2CaCu2O8+δ phonons contribute ∼ 10% and non-phononic excitations ∼ 90%.Experimental evidence based on the analysis of the optical properties of the high T c cuprate superconductors suggested early on that the charge carriers were strongly coupled to a spectrum of bosonic excitations in the 40 to 60 meV range [1,2]. This was confirmed by the discovery of a slope change or kink in electronic dispersion of the quasiparticles (QP) by angle resolved photoemission spectroscopy (ARPES) in the same energy range [3][4][5]. The boson coupling that manifests itself as peaks in the real part of the QP self energy extracted from the ARPES dispersion curves can be seen in optical spectroscopy as features in the optical scattering rate, a term in the generalized Drude formula for the optical conductivity [1,2,9,12,17,[19][20][21] and in tunneling [27,28]. Surprisingly, the nature of the bosons involved remains highly controversial [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. The subject is of great interest since such a coupling, would give us a working model of superconductivity in these materials, at least within the Migdal-Eliashberg formalism with retarded interactions. In support of this approach, recent numerical solutions of the Mott-Hubbard model suggest that in the high T c cuprates retarded interactions do provide most of the pairing [22,23], with the energy scale set by the size of the antiferromagnetic exchange constant J. These calculations do not support the suggestion by Anderson [24] that the energy scale for the retardation might be much higher and set by the Hubbard U which would imply non-retarded pairing. Another mechanism considered in the literature is kinetic energy pairing for which the kinetic rather than the potential energy is lowered as the temperature is lowered below T c . In an Eliashberg formalism this can be simulated by a phenomenological reduction in quasiparticle scattering which could be due to a reduction in the electron-boson spectral density [25,26]. But this, presumably, applies only to the superconducting state and would give no dispersion 'kink' above T c .The controversy over the bosonic spectrum centers on the nature of the bosons: are they p...

An electron–boson glue function derived from electronic Raman scattering

“…Recent ARPES experiments along the nodal direction 16 found a shift in the 'boson kink' in the renormalized dispersion curves of Bi2212 upon oxygen isotope substitution. This was assigned by Schachinger et al 15 as a 10% phonon contribution to the electron-boson spectral density found in inversions 10 of ARPES data as reproduced in Fig. 1(d).…”

“…For nodal ARPES there is no peak at ∼ 30 meV but one appears instead at much higher energy ∼ 65 meV. This higher energy has often been identified with coupling to oxygen phonons [4][5][6]15,16 and we will return to this issue later. Such a peak is not seen in our Raman spectra which indicates that such effects are mainly confined to the nodal direction and do not appear in averaged quantities such as B 1g and even B 2g Raman even though for this latter polarization the Raman vertex peaks in the nodal direction.…”

Large momentum-dependence of the main dispersion ‘kink’ in the high-Tcsuperconductor Bi2Sr2CaCu2O8+δ

“…A very detailed low-hν ARPES study found an isotope shift in the energy of the nodal kink [19], giving strong merit to the phonon scenario. One possible explanation for this conflict is that electron-phonon interactions might constitute a finite but relatively small contribution to the total self-energy [49]. Alternatively, the results may signal a role for coupling between spin and lattice degrees of freedom [50][51][52].…”

Disentangling the Electronic and Phononic Glue in a High- T c Superconductor

“…An isotope effect in the dispersion of nodal QPs has been recently reported on optimally-doped Bi2212, by ARPES measurements [32]. These data have been carefully analyzed [33], demonstrating that the nodal isotope effect can be explained assuming that the QP-phonon coupling represents about 10% of the total contribution of other bosonic excitations. From Figure 3, we estimate that the contribution of SCP is less than 20% of the total bosonic function.…”