Electron–Phonon Interaction and Lattice Dynamics in High T_c Superconductors

The following sections are included:

• Contents
• Preface

In this colloquium, the main features of the electron–lattice interaction are discussed and high values of the critical temperature up to room temperature could be provided. While the issue of the mechanism of superconductivity in the high-T_c cuprates continues to be controversial, one can state that there have been many experimental results demonstrating that the lattice makes a strong impact on the pairing of electrons. The polaronic nature of the carriers is also a manifestation of strong electron–lattice interaction. One can propose an experiment that allows an unambiguous determination of the intermediate boson (phonon, magnon, exciton, etc.) which provides the pairing. The electron–lattice interaction increases for nanosystems, and this is due to an effective increase in the density of states.

With its central role in conventional BCS superconductivity, electron-phonon coupling appears to play a more subtle role in the phase diagram of the high-temperature superconducting cuprates. Their added complexity due to potentially numerous competing phases, including charge, spin, orbital, and lattice ordering, makes teasing out any unique phenomena challenging. In this review, we present our work using angle-resolved photoemission spectroscopy (ARPES) exploring the role of the lattice on the valence band electronic structure of the cuprates. We introduce the ARPES technique and its unique ability to the probe the effect of bosonic renormalization (or “kink”) on near-E_F band structure. Our survey begins with the establishment of the ubiquitous nodal cuprate kink leading to how isotope substitution has shed a critical new perspective on the role and strength of electron–phonon coupling. We continue with recently published work connecting the phonon dispersion seen with inelastic X-ray scattering (IXS) to the location of the kink observed by ARPES near the nodal point. Finally, we present very recent and ongoing ARPES work examining how induced strain through chemical pressure provides a potentially promising avenue for understanding the broader role of the lattice to the superconducting phase and larger cuprate phase diagram.

This paper gives a summary of inelastic neutron scattering studies searching for signatures of a strong electron–phonon coupling in high-temperature superconductors. Special emphasis is laid on the anomalous dispersion, the unusually large linewidths and the anomalous temperature dependence observed for plane polarized copper-oxygen bond-stretching vibrations. It will be discussed in how far these results can be understood within conventional density functional theory or require recourse to theories for strongly correlated electrons, in particular the concept of charge stripe order.

Stripe order where electrons self-organize into alternating periodic charge-rich and magnetically-ordered charge-poor parallel lines was proposed as a way of optimizing the kinetic energy of holes in a doped Mott insulator. Static stripes detected as extra peaks in diffraction patterns, appear in a number of oxide perovskites as well as some other systems. The more controversial dynamic stripes, which are not detectable by diffraction, may be universally present in copper oxide superconductors. Thus it is important to learn how to detect dynamic stripes as well as to understand their influence on electronic properties. This review article focuses on lattice vibrations (phonons) that might show signatures of the charge component of dynamic stripes. The first part of the article describes recent progress in learning about how the phonon signatures of different types of electronic charge fluctuations including stripes can be distinguished from purely structural instabilities and from each other. Then I will focus on the evidence for dynamic stripes in the phonon spectra of copper oxide superconductors.

The planar oxygen isotope effect coefficient measured as a function of hole doping in the Pr- and La-doped YBa₂Cu₃O₇ (YBCO) and the Ni-doped La_1.85Sr_0.15CuO₄ (LSCO) superconductors quantitatively and qualitatively follows the form originally proposed by Kresin and Wolf [Phys. Rev. B 49, (1994) 3652], which was derived for polarons perpendicular to the superconducting planes. Interestingly, the inverse oxygen isotope effect coefficient at the pseudogap temperature also obeys the same formula. These findings allow the conclusion that the superconductivity in YBCO and LSCO results from polarons or rather bipolarons in the CuO₂ plane. The original formula, proposed for the perpendicular direction only, is obviously more generally valid and accounts for the superconductivity in the CuO₂ planes.

Oxygen isotope effects on T_c and the Meissner fraction f have been investigated in fine-grained, decoupled La_2−xSr_xCuO₄ with x = 0.105, 0.110, and 0.115. We find that these oxygen isotope effects are related to each other: d ln T_c/d ln M ≈ d ln f/d ln M (where M is the mass of oxygen). We also show that the trapped flux due to intergrain weak-link and intragrain flux pinning is negligible in our samples, and that the Meissner fractions for the samples with the same 16_O isotope are nearly equal The observed large oxygen isotope effects on T_c and the Meissner fraction can be explained as due to the oxygen-mass dependence of m* (effective mass of carriers). The results may suggest that the conducting carriers in the cuprate superconductors are of polaronic type.

We have studied the oxygen-isotope effects on T_c and in-plane penetration depth λ_ab(0) in an optimally doped three-layer cuprate Bi_1.6Pb_0.4Sr₂Ca₂Cu₃O_10+y(T_c ∼ 107 K). We find a small oxygen-isotope effect on T_c(α_O = 0.019), and a substantial effect on λ_ab(0)[Δλ_ab(0)/λ_ab(0) = 2.5 ± 0.5%]. The present results along with the previously observed isotope effects in single-layer and double-layer cuprates indicate that the isotope exponent α_O in optimally doped cuprates is small while the isotope effect on the in-plane effective supercarrier mass is substantial and nearly independent of the number of the CuO₂ layers. A plausible pairing mechanism is proposed to explain the isotope effects, high-T_c superconductivity, and tunneling spectra in a consistent way.

Angle-resolvedphotoemission spectroscopy with low-energy tunable photons along the nodal direction of oxygen isotope substituted Bi₂Sr₂CaCu₂O_8+δ reveals a distinct oxygen isotope shift near the electronboson coupling “kink” in the electronic dispersion. The magnitude (afew meV) and direction of the kink shift are as expected due to the measured isotopic shift of phonon frequency, and are also in agreement with theoretical expectations. This demonstrates the participation of the phonons as dominant players, as well as pinpointing the most relevant of the phonon branches.

We investigate the electronic dispersion of high-T_c superconductor on the basis of the 2D three-band Hubbard model with the electron–phonon interaction (EPI) together with the strong electron–electron interaction (EEI). In our model, it is shown across the hole-doped region of high-T_c superconductor that the EPI makes a dispersion kink, observed along the nodal direction, and that the small isotope effect appears on the electronic dispersion.

Many high-temperature superconductors are highly polarizable ionic lattices where the Fröhlich electron–phonon interaction (EPI) with longitudinal optical phonons creates an effective attraction of doped carriers virtually equal to their Coulomb repulsion. The general multipolaron theory is given with both interactions being strong compared with the carrier kinetic energy so that the conventional BCS-Eliashberg approximation is inapplicable. The many-electron system is described by the polaronic t−J_p Hamiltonian with reduced hopping integral, t, allowed double on-site occupancy, large phonon-induced anti-ferromagnetic exchange, J_p ≫ t, and a high-temperature superconducting state of small superlight bipolarons protected from clustering.

Soon after the discovery of the first high-temperature superconductor by Georg Bednorz and Alex Müller in 1986, the late Sir Nevill Mott in answering his own question ‘Is there an explanation?’ (Nature 327 (1987), 185) expressed the view that the Bose–Einstein condensation (BEC) of small bipolarons, predicted by us in 1981, could be the one. Several authors then contemplated BEC of realspace tightly bound pairs, but with a purely electronic mechanism of pairing rather than with an electron–phonon interaction (EPI). However, a number of other researchers criticized the bipolaron (or any real-space pairing) scenario as incompatible with some angle-resolved photoemission spectra, with experimentally determined effective masses of carriers and unconventional symmetry of the superconducting order parameter in cuprates. Since then, the controversial issue of whether EPI is crucial for high-temperature superconductivity or is weak and inessential has been one of the most challenging problems of contemporary condensed matter physics. Here I outline some developments in the bipolaron theory suggesting that the true origin of high-temperature superconductivity is found in a proper combination of strong electron–electron correlations with a significant finite-range (Fröhlich) EPI, and that the theory is fully compatible with key experiments.

The crystal lattice of a complex compound may contain a subsystem of ions with each one possessing two close equilibrium positions (double-well structure). For example, the oxygen ions in the cuprates form such a subsystem. In such a situation, it is impossible to separate electronic and local vibrational motions. This leads to a large increase in the effective strength of the electron–lattice interaction, which is beneficial for pairing.

We reanalyze high-resolution scanning tunneling spectra of the electron-doped cuprate Pr_0.88LaCe_0.12CuO₄ (T_c = 24K). We find that the spectral fine structure below 35 meV is consistent with strong coupling to a bosonic mode at about 16 meV, in quantitative agreement with early tunneling spectra of Nd_1.85Ce_0.15CuO₄. Since the energy of the bosonic mode is significantly higher than that (9.5–11 meV) of the magnetic resonancelike mode observed by inelastic neutron scattering, the coupling feature at about 16meV cannot arise from strong coupling to the magnetic mode. The present work thus demonstrates that the magnetic resonancelike mode cannot be the origin of high-temperature superconductivity in electron-doped cuprates.

We identify the intrinsic bulk pairing symmetry for both electron- and hole-doped cuprates from the existing bulk-and nearly bulk-sensitive experimental results such as magnetic penetration depth, Raman scattering, single-particle tunneling, Andreev reflection, nonlinear Meissner effect, neutron scattering, thermal conductivity, specific heat, and angle-resolved photoemission spectroscopy. These experiments consistently show that the dominant bulk pairing symmetry in hole-doped cuprates is of extended s wave with eight line nodes and of anisotropic s wave in electron-doped cuprates. The proposed pairing symmetries do not contradict some surface- and phase-sensitive experiments that show a predominant d-wave pairing symmetry at the degraded surfaces. We also quantitatively explain the phase-sensitive experiments along the c axis for both Bi₂Sr₂CaCu₂O_8+y and YBa₂Cu₃O_7−y.

All the high T_c superconductors are structurally composed of two different blocks, the perovskite, and the rock salt. The perovskite block is the active block where the Cu(2)–O planes are located and the carriers concentrate. The rock salt block corresponds to the charge-reservoir block, which supplies the carriers to the Cu(2)–O planes. Based on this fact, we developed a model to calculate the interaction between the two blocks (marked by combinative energy) and to study their relationship with the value of T_c. Bi-system superconductors, (such as Bi₂Sr₂CuO_y, Bi₂Sr₂CaCu₂O_y and Bi₂Sr₂Ca₂Cu₃O_y), Hg-system superconductors (such as HgBa₂CuO_y, HgBa₂CaCu₂O_y, HgBa₂Ca₂Cu₃O_y, HgBa₂Ca₃Cu₄O_y and HgBa₂Ca₄Cu₅O_y), Tl-system superconductors (such as Tl₂Ba₂Ca_n−1Cu_nO_2n+3 with 5 superconductive compounds and Tl₂Ba₂Ca_n−1Cu_nO_2n+4 with 4 superconductive compounds), Y-system superconductors with different oxygen deficiencies, and La_2−xM_xCuO₄ (M=Ba, Sr) with different M concentrations, were studied with our model, respectively. A close relationship between the superconducting transition temperature and the combinative energy in these superconducting systems is established, i.e., the higher the combinative energy is, the lower the T_c value is. Furthermore, it is discovered by X-ray analysis and Raman spectroscopy that the Cu(2)-O plane located in the boundary of the two blocks is very steady, i.e., the bond lengths and angles in this plane are hardly changed and form a so-called “fixed triangle”. This fixed triangle may be in charge of the strong anisotropy of the high T_c superconductors. It is suggested that because of the very strong anisotropy, not only the energy, but the anisotropy of phonons should be taken into account. Under this strong anisotropy, the state of the carrier may be changed or polarized, and then determines the superconductivity. The strong anisotropy of phonons may be the main difference between the conventional superconductors and the high T_c superconductors. The results show that the lattice dynamics or electron–phonon interaction is still of great importance for high T_c superconductivity.

The following section is included:

• Index