Electron Correlation and High-Temperature Superconductivity

Much theoretical work has been devoted to understanding the role of strong electron correlations in high-temperature superconductivity mainly through magnetic interactions, but the possible role of electron correlation in ferroelectricity of metal oxides has not received attention. Diagonalization of a simple many-body, tight-binding Hamiltonian shows that the electron-lattice interaction is dramatically enhanced in some cases by strong electron correlation because of deformation-induced charge transfer. This effect may be closely related to ferroelectricity and superconductivity in transition metal oxides.

Some of the early models of high temperature superconductivity (HTS) in cuprates dismissed a pairing mechanism based on electron–phonon (e–ph) interactions. One of the arguments against the e–ph theories was the negligible isotope effect on the critical temperature, T c. Other arguments were based on approximations performed near the strong e–ph interaction regime in which HTS might take place1. This leads to the conclusion that an e–ph paring is inoperative. As a result, pure electron correlations, excitonic mechanisms and spin fluctuations have attracted most of the attention, overshadowing the e–ph approaches. However, some of the features shown by copper oxides seem to validate the e–ph models, in particular those which concern small bipolarons and the Jahn–Teller (JT) effect. For instance, these materials have a bandwidth within a range where the strength of JT coupling is important. Nonadiabatic effects cannot be ignored when high frequency phonons are coupled to itinerant charges. Therefore, theories based on on-site or intersite bipolarons, JT bipolarons and different mechanisms of carrier dynamics, such as Bose-Einstein condensation and tunneling-percolation, have been proposed. However, our discussion is centered on the JT models and the intriguing possibility that HTS could be driven by JT forces. The JT models have several distinctive features: they deal with a multidimensional electron basis coupled to symmetric phonon degrees of freedom. Moreover, JT Polarons exhibit strong anharmonicity. The review highlights these local constraints and their consequences for the dynamics of polaron formation, the appearance of an inhomogeneous state and charge transport properties. In addition, the broken local symmetry at the thermodynamic limit of interacting JT polarons, when it is combined with long range Coulomb interactions, leads to specific macroscopic manifestations. Thus, cooperative effects go beyond standard structural transitions, and a novel organization of nanoscopic textures is manifested. Here we also address this issue and its connection with HTS, e.g. whether the so-called pseudogap observed in cuprates is related to the energy scale of the JT-bipolaron formation and the phase-segregation phase.

Superconductivity in the iron pnictides and chalcogenides is closely connected to a bad-metal normal state and a nearby antiferromagnetic order. Therefore, considerable attention has been focused on the role of electron correlations and spin dynamics. In this article, we summarize some key experiments that quite directly imply strong electron correlations in these materials, and discuss aspects of the recent theoretical studies on these issues. In particular, we outline a w-expansion, which treats the correlation effects using the Mott transition as the reference point. For the parent systems, it gives rise to an effective J1-J2 model that is coupled to the itinerant electrons in the vicinity of the Fermi energy; this model yields an isoelectronically-tuned quantum critical point, and allows a study of the distribution of the spin spectral weight in the energy and momentum space in the paramagnetic phase. Within the same framework, we demonstrate the Mott insulating phase in the iron oxychalcogenides as well as the alkaline iron selenides; for the latter system, we also consider the role of an orbital-selective Mott phase. Finally, we discuss the singlet superconducting pairing driven by the short-range J1-J2 interactions. Our considerations highlight the iron pnictides and chalcogenides as exemplifying strongly-correlated electron systems at the boundary of electronic localization and itinerancy.

In opening the Levico BEC 2003 meeting, the directors thought it would be useful to say a little about the first BEC workshop held in the same hotel, in the same lecture room, almost exactly ten years ago. I want to give you a personal view of what led up to the historic BEC 93 workshop at Levico and contrast the situation then with the fantastic developments which have occurred over the last decade. BEC 93 was organized by Griffin, Snoke, Stringari, Laloe and Baym. The purpose of the workshop was to bring together people working in different fields of physics but with a common interest in the phenomenon of Bose–Einstein condensation. It is useful to briefly recall the history of BEC studies before the BEC 93 workshop, to understand why it was organized.

High-Temperature Superconductivity in Strongly Correlated Electronic Systems

Liquids and gases are distinct in their extent of dynamic atomic correlations; in gases, atoms are almost uncorrelated, whereas they are strongly correlated in liquids. This distinction applies also to electronic systems. Fermi liquids are actually gas-like, whereas strongly correlated electrons are liquid-like. Doped Mott insulators share characteristics with supercooled liquids. Such distinctions have important implications for superconductivity. We discuss the nature of dynamic atomic correlations in liquids and a possible effect of strong electron correlations and Bose–Einstein condensation on the high-temperature superconductivity of the cuprates.

ABSTRACTMolecules characterized by an inverted singlet‐triplet gap (ΔEST<0) hold potential for optoelectronic applications. Electronic correlation and environmental polarization are key factors influencing negative ΔEST, and the latter is gaining attention for its possible role in “mimicking” correlation contributions to yield negative ΔEST. However, a comprehensive study of solvation effects on both structures and energy gaps is still lacking. In this work, we evaluate computational strategies for calculating ΔEST<0 gaps, incorporating electronic correlation and solvent polarization in molecules exhibiting singlet‐triplet inversion. Using RMS–CASPT2 as a benchmark, we demonstrate that double‐hybrid density functionals and mixed‐reference spin‐flip TD‐DFT (MRSF–TD‐DFT) can partially recover electronic correlation. Furthermore, we investigate solvation effects on both singlet and triplet excited states, highlighting the limitations of linear‐response schemes in continuum solvation models. We finally develop a protocol combining electronic correlation and state‐specific solvent polarization using double‐hybrid functionals and the Vertical Excitation Model (VEM), leveraging its Lagrangian implementation to compute structures and adiabatic energies. Applying our B2PLYP/VEM(UD) protocol to larger systems with experimentally observed negative ΔEST gaps, we quantitatively reproduce experimental emissive and non‐radiative transition rates.

The role of electron correlation on different pairing symmetries are discussed in details where the electron correlation has been treated within the slave boson formalism. It is shown that for a pure $s$ or pure $d$ wave pairing symmetry, the electronic correlation suppresses the $s$ wave gap magnitude (as well as the $T_c$) at a faster rate than that for the $d$ wave gap. On the otherhand, a complex order parameter of the form ($s+id$) shows anomalous temperature dependence. For example, if the temperature ($T_{c}^d$) at which the $d$ wave component of the complex order parameter vanishes happens to be larger than that for the $s$ wave component ($T_{c}^s$) then the growth of the $d$ wave component is arrested with the onset of the $s$ wave component of the order parameter. In this mixed phase however, we find that the suppression in different components of the gap as well as the corresponding $T_c$ due to coulomb correlation are very sensitive to the relative pairing strengths of $s$ and $d$ channels as well as the underlying lattice. Interestingly enough, in such a scenario (for a case of $T_{c}^s > T_{c}^d$) the gap magnitude of the $d$ wave component increases with electron correlation but not $T_{c}^d$ for certain values of electron correlation. However, this never happens in case of the $s$ wave component. We also calculate the temperature dependence of the superconducting gap along both the high symmetry directions ($\Gamma$ - M and $\Gamma $ - X) in a mixed $s+id$ symmetry pairing state and the thermal variation of the gap anisotropy ($\frac{\Delta_{\Gamma - M}}{\Delta_{\Gamma - X}}$) with electron correlation. The results are discussed with reference to experimental observations.

XH-stretching vibrational band intensities have been calculated for seven small molecules with OH, NH and CH bonds, respectively, using the simple harmonically coupled anharmonic oscillator local mode model and ab initio dipole moment functions, both expressed in XH-stretching bond coordinates. The dipole moment functions were calculated with a triple valence basis set including both diffuse and multiple polarization functions, and at different levels of ab initio theory. The self-consistent field Hartree-Fock calculation is compared with different ways of including electron correlation. These calculations show that in general electron correlation in the ab initio calculation of the dipole moment function is often important in predictions of fundamental XH-stretching band intensities, whereas the XH-stretching overtone intensities are insensitive to electron correlation. This insight is important for studies of larger molecules where the highest levels of theory are not computationally feasible.

XH-stretching vibrational band intensities have been calculated for seven small molecules with OH, NH and CH bonds, respectively, using the simple harmonically coupled anharmonic oscillator local mode model and ab initio dipole moment functions, both expressed in XH-stretching bond coordinates. The dipole moment functions were calculated with a triple valence basis set including both diffuse and multiple polarization functions, and at different levels of ab initio theory. The self-consistent field Hartree-Fock calculation is compared with different ways of including electron correlation. These calculations show that in general electron correlation in the ab initio calculation of the dipole moment function is often important in predictions of fundamental XH-stretching band intensities, whereas the XH-stretching overtone intensities are insensitive to electron correlation. This insight is important for studies of larger molecules where the highest levels of theory are not computationally feasible.

Localization and electron correlation play significant roles in understanding the electronic states of low-dimensional systems. We carried out the tunneling spectroscopy measurements on a crystalline nano-sized island and a disordered two-dimensional metal film. The low temperature zero-bias anomaly was studied using theory and statistical analysis of the spatial distribution of the local density of states in both the systems. The effective capacitance and resistance of the tunnel junction extracted from theory gives the energy and temperature dependency of the measured ZBA. Statistical analysis reveals the electron correlation effect and the electron correlation length. By combining theory and the statistical analysis, we found that the microscopic origin of ZBA formation in the disordered two-dimensional film is strongly related to the electron localization and the correlations.

The Compton profiles (CP) of crystalline urea are computed ab initio at different levels of theory and compared with accurate experimental measurements. The CRYSTAL program is used in order to collect the Hartree-Fock (HF) and density-functional theory (DFT) results, while the new CRYSCOR code is adopted for the calculation of the MP2 correction to the HF density matrix. It is demonstrated that the role of electron correlation (Fermi and Coulomb) is crucial in predicting the correct CPs; DFT is shown to provide results in partial disagreement with the experiment, at variance with the HF/MP2 treatment that correctly predicts the CP anisotropies of urea. We demonstrate that the global effect of dynamic electron correlation is the reduction of the anisotropy of the electronic momentum distribution within the crystal.

High-temperature superconductivity in cuprates remains a central challenge in condensed matter physics due to the complex interplay of lattice dynamics and electronic correlations. Traditional BCS theory fails to capture these effects, while competing models emphasize either phonons or correlations but rarely both. We propose a novel Hamiltonian that integrates linear and quadratic phonon-mediated interactions with strong electronic correlations in a two-dimensional cuprate lattice, representing the first unified framework incorporating quadratic electron-phonon coupling (QEPC) for enhanced pairing. This innovation addresses limitations in prior models by including multiple phonon modes, momentum-dependent coupling, and QEPC, which enables quantum bipolaron formation and significantly boosts T_c. Through rigorous derivations using extended Eliashberg equations, we obtain analytical and numerical expressions for the critical temperature (T_c) and superconducting gap (Delta), incorporating a frequency- and momentum-dependent pairing potential enhanced by QEPC, absent in prior models. Our proofs elucidate the synergy between linear/quadratic electron-phonon coupling (g, gamma) and on-site repulsion (U), predicting enhanced T_c up to approx 100 K in cuprates, surpassing previous limits, along with a dome-shaped phase diagram peaking at optimal doping. Numerical simulations, with improved self-consistent solutions and larger grids, validate these results against experimental data, revealing non-monotonic trends in T_c and Delta with respect to g, gamma, and doping x, as well as a doping-dependent isotope coefficient that minimizes at optimal doping and increases in the underdoped and overdoped regimes. This unified framework bridges phonon- and correlation-driven mechanisms, offering novel insights for material design, such as engineered superlattices for QEPC, and resolving longstanding controversies in high-T_c superconductivity by predicting higher T_c through quantum effects.

Since the discovery of high Tc superconductivity, the role of electron correlation on superconductivity has been an important issue in condensed matter physics. Here the role of electron correlation in metals is explained in detail on the basis of the Fermi liquid theory. The book, originally published in 2004, discusses the following issues: enhancements of electronic specific heat and magnetic susceptibility, effects of electron correlation on transport phenomena such as electric resistivity and Hall coefficient, magnetism, Mott transition and unconventional superconductivity. These originate commonly from the Coulomb repulsion between electrons. In particular, superconductivity in strongly correlated electron systems is discussed with a unified point of view. This book is written to explain interesting physics in metals for undergraduate and graduate students and researchers in condensed matter physics.

The discovery of superconductivity in planar nickelates raises the question of how the electronic structure and correlations of Ni1+ compounds compare to those of the Cu2+ cuprate superconductors. Here, we present an angle-resolved photoemission spectroscopy (ARPES) study of the trilayer nickelate Pr4Ni3O8, revealing a Fermi surface resembling that of the hole-doped cuprates but with critical differences. Specifically, the main portions of the Fermi surface are extremely similar to that of the bilayer cuprates, with an additional piece that can accommodate additional hole doping. We find that the electronic correlations are about twice as strong in the nickelates and are almost k-independent, indicating that they originate from a local effect, likely the Mott interaction, whereas cuprate interactions are somewhat less local. Nevertheless, the nickelates still demonstrate the strange-metal behavior in the electron scattering rates. Understanding the similarities and differences between these two families of strongly correlated superconductors is an important challenge.