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In this paper we discuss experimental evidence related to the
structure and origin of the bosonic spectral function

In spite of an unprecedented intensive experimental and theoretical study after the discovery of high-temperature superconductivity (HTSC) in cuprates, there is, even twenty-three years after, no consensus on the pairing mechanism in these materials. At present there are two important experimental facts which are not under dispute: (

There are at least two approaches differing in assumed pairing bosons in the HTSC cuprates. The

The

Since

The paper is organized as follows. In Section

(a)

(b)

(c)

(d)

(e)

In Section

Finally, one can pose a question—do the experimental results of the above enumerated spectroscopic methods allow a building of a satisfactory and physically reasonable microscopic theory for basic scattering and pairing mechanism in cuprates? The posed question is very modest compared to the much stringent request for the

The microscopic theory of the mechanism for superconducting pairing in HTSC cuprates will be discussed in Section

Finally, we would like to point out that in real HTSC materials there are numerous experimental evidences for nanoscale inhomogeneities. For instance, recent STM experiments show rather large gap dispersion, at least on the surface of BSCO crystals [

Concerning the high

After discovery of HTSC in cuprates there was a large amount of evidence on strong scattering of quasiparticles which contradicts the canonical (popular but narrow) definition of the Fermi liquid, thus giving rise to numerous proposals of the so called non-Fermi liquids, such as Luttinger liquid, RVB theory, marginal Fermi liquid, and so forth. In our opinion there is no need for these radical approaches in explaining basic physics in cuprates at least

In spite of the reached experimental evidence in favor of strong EPI in HTSC oxides, there was a disproportion in the research activity (especially theoretical) in the past, since the investigation of the SFI mechanism of pairing prevailed in the literature. This trend was partly due to an incorrect statement in [

It is well known that in an electron-ion crystal, besides the attractive EPI, there is also repulsive Coulomb interaction. In case of an isotropic and homogeneous system with weak quasiparticle interaction, the effective potential

Moreover, the basic theory tells us that

Inverse total static dielectric function

The above analysis tells us that in real crystals

In conclusion, we point out that there are no serious theoretical and experimental arguments for ignoring EPI in HTSC cuprates. To this end it is necessary to answer several important questions which are related to experimental findings in HTSC cuprates. (

Regarding EPI one can pose a question about whether it contributes significantly to

Concerning other nonphononic mechanisms, such as the SFI one, the effect of EPI in the framework of Eliashberg equations was studied numerically in [

In the following we discuss some important experiments which give evidence for strong electron-phonon interaction (EPI) in cuprates. However, before doing it, we will discuss some indicative

Before discussing experimental results in cuprates on the imaginary part of the spin susceptibility

Can the pairing mechanism in HTSC cuprates be explained by such a phenomenology and what is the prise for it is? The best answer is to look at the experimental results related to the inelastic magnetic neutron scattering (IMNS) which gives

Magnetic spectral function

The most pronounced result for our discussion is that by varying doping

Having in mind the results in [

Concerning the problem related to the rearrangement of the SFI spectral function

A less direct argument for

Magnetic spectral function

After the discovery of the resonance peak there were attempts to relate it, first, to the origin of the superconducting condensation energy and, second, to the kink in the energy dispersion or the peak-dimp structure in the ARPES spectral function. In order that the condensation energy is due to the magnetic resonance, it is necessary that the peak intensity

Finally, we would like to point out that the recent magnetic neutron scattering measurements on optimally doped large-volume crystals

Optical spectroscopy gives information on

The widespread misconception in studying the quasiparticle scattering in cuprates was an ad hoc assumption that the

The dynamical conductivity

(a) Scattering rates

The results shown in Figure

Let us discuss briefly the experimental results for

(a) Experimental transport scattering rate

Now we will comment the so called pronounced linear behavior of

Dependence of

However, in some experiments [

Furthermore, we would like to comment two points related to

In principle, the transport spectral function

Experimental (solid lines) and calculated (dashed lines) data of

Experimental (solid line) and calculated (dashed line) data of

These results demonstrate the importance of EPI in cuprates [

To this end, we would like to comment two aspects which appear from time to time in the literature.

Finally, we point out that very similar (to cuprates) properties, of

The

The

Let us enumerate and discuss the

Measured spectral weight

However, in some optimally doped and in most overdoped cuprates, there is a decrease of

(a) Spectral weight

We stress that the non-BCS behavior of

The first question is the following. How to explain the strong temperature dependence of

Spectral weight

To summarize, the above analysis demonstrates that the theory based on EPI is able to explain in a satisfactory way the temperature behavior of

The temperature dependence of the in-plane resistivity

(a) Calculated resistivity

There is experimental constraint on

Transport EPI spectral function coupling constant in YBCO as a function of plasma frequency

Concerning the temperature dependence of the resistivity in other (than YBCO) families of the optimally doped HTSC cuprates we would like to point out that there is some evidence that the linear (in

The femtosecond time-resolved optical spectroscopy (FTROS) has been developed in the last couple of years and applied to HTSC cuprates. In this method a femtosecond (

The angle-resolved photoemission spectroscopy (ARPES) is nowadays one of leading spectroscopy methods in the solid-state physics [

ARPES measures a nonlinear response function of the electron system and it is usually analyzed in the so-called

(

(top) Quasiparticle dispersion of

(ii) The kink structure is observed in a variety of the hole-doped cuprates such as

(a) Effective real self-energy for the nonsuperconducting

The latter result is in a qualitative agreement with numerous tunnelling measurements [

Figure 4b from [

It is seen that

(a) The ARPES spectrum of undoped

However, the peak in Figure

NCCO electron-doped: (a)

It is seen from this figure that the effective EPI coupling constant

(

Crystal structure of

(a) Fermi surface (FS) contours from two samples of F0234.

In conclusion, in order to explain the ARPES results in cuprates it is necessary to take into account (

By measuring current-voltage

From tunnelling experiments one obtains the (energy-dependent) gap function

Here we are interested in the

(a) Second derivative of

The tunnelling spectra in Bi-2212 break junctions [

The spectral functions

These results show very similar features to those obtained in [

The spectral functions

In that respect, the tunnelling measurements on

Phonon frequency _{2}Sr_{2}CaCu_{2}O_{8}.

No. of peak | |||
---|---|---|---|

14.3 | 1.26 | 7.4 | |

20.8 | 0.95 | 11.0 | |

31.7 | 0.48 | 10.5 | |

35.1 | 0.28 | 6.7 | |

39.4 | 0.24 | 7.0 | |

45.3 | 0.30 | 10.0 | |

58.3 | 0.15 | 6.5 | |

63.9 | 0.01 | 0.6 | |

69.9 | 0.07 | 3.6 | |

73.7 | 0.06 | 3.3 | |

77.3 | 0.01 | 0.8 | |

82.1 | 0.01 | 0.7 | |

87.1 | 0.03 | 1.8 |

The spectral functions

The next remarkable result is that the extracted

Let us discuss the content of Table

The phonon density of states

Atomic polarization vectors and their frequencies (in

Atomic polarization vectors and their frequencies (in

Further, based on Table

Similar conclusion regarding the structure of the

(a)

Note that the BTK parameter

Although most of the peaks in

Doping dependence of the energy

This means that if one of the peaks in

Second derivative of

The presence of pronounced phononic structures (and the importance of EPI) in the

Second derivative data

It is interesting that in the

(a) Typical conductance

It turns out that the corresponding average phonon energy

The important message of numerous tunnelling experiments in

Although experiments related to phonon spectra and their renormalization by

The phonon Green's function

The appreciable softening and broadening of numerous phonon modes has been observed in the normal state of HTSC cuprates, thus giving evidence for pronounced EPI effects and for inadequacy of the LDA-DFT calculations in treating strong correlations and suppression of the charge susceptibility [

Comparison of DFT calculations with experimental results of inelastic X-ray scattering: (a) phonon energies in

In Section

The

The isotope effect

This problem will be discussed only briefly since more extensive discussion can be found in [

The fine structure of the quasiparticle self-energy

(a) Effective

By analyzing the shift in Im

The analysis of experimental data in HTSC cuprates which are related to optics, tunnelling, and ARPES measurements

The ineffectiveness of SFI to solely provide pairing mechanism in cuprates comes out also from the magnetic neutron scattering on YBCO and BSCO. As a result, the imaginary part of the susceptibility is drastically reduced in the low-energy region by going from slightly underdoped toward optimally doped systems, while

Inelastic neutron and X-ray scattering measurements in HTSC cuprates show that the broadening of some phonon lines is by an order of magnitude larger than the LDA-DFA methods predict. Since the phonon line-widths depend on the EPI coupling and the charge susceptibility, it is evident that calculations of both quantities are beyond the range of applicability of LDA-DFT. As a consequence, the LDA-DFT calculations overestimate the electronic screening and thus underestimate the EPI coupling, since many-body effects due to strong correlations are not contained in this mean-field theory. However, in spite of the promising and encouraging experimental results about the dominance of EPI in cuprates, the theory is still confronted with difficulties in explaining sufficiently large coupling constant in the

The experimental results in Section

In the case of very complicated systems, such as the HTSC cuprates, the standard (pragmatical) procedure in physics is to formulate a minimal theoretical model—sometimes called toy model—which includes minimal set of important ingredients necessary for qualitative and semiquantitative study of a phenomenon. As a consequence of the experimental results

Finally, by writing this chapter our intention is not to overview the theoretical studies of EPI in HTSC cuprates—which is an impossible task—but first to elucidate the descending way from the (old) well-defined ab initio microscopic theory of superconductivity to the one of the minimal model which treats the interplay of EPI and strong correlations. Next, we would like to encourage the reader to further develop the theory of HTSC cuprates.

The many-body theory of superconductivity is based on the fully microscopic electron-ion Hamiltonian for electrons and ions in the crystal—see, for instance, [

Dyson's equations for the electron and phonon Green's functions

If the vertex function

The procedure of separating low-energy and high-energy processes lies also behind the

It is well known that the Coulomb self-energy

Finally, we obtain the matrix Dyson equation for the renormalized Green's function

The important ingredients of the low-energy Migdal-Eliashberg theory are the ideal band-structure Hamiltonian

After solving (

We point out again two results which are important for the future microscopic theory of pairing in HTSC cuprates.

The main task of the LDA-DFT theory in obtaining the EPI matrix elements is to calculate the change of the ground-state (self-consistent) potential