Beyond on-site Hubbard interaction in charge dynamics of cuprate superconductors

TL;DR

This review argues that long-range Coulomb interactions (LRC) are essential for understanding charge dynamics in cuprate superconductors. It introduces a layered $t$-$J$-$V$ model that couples standard short-range physics to interlayer Coulomb terms, predicting plasmon bands and plasmarons that reshape the electron self-energy and spectral function. The framework connects high-energy plasmon phenomena to low-energy Fermi-liquid behavior in the overdoped regime, while incorporating a pseudogap description through a minimal self-energy and showing how charge fluctuations interact with spin fluctuations to realize or suppress superconductivity. It further extends to bilayer systems, reproduces RIXS data, and demonstrates that screening of nearest-neighbor Coulomb interactions can play a constructive role in high-$T_c$ pairing within a spin-fluctuation–driven mechanism. Overall, the work establishes a cohesive picture linking plasmons, pseudogap physics, and high-$T_c$ superconductivity in layered cuprates and suggests broader applicability to other correlated materials.

Abstract

In this review, we first present compelling evidence from resonant inelastic x-ray scattering data that highlights the significance of the long-range Coulomb interaction in cuprate charge dynamics, particularly around the in-plane momentum q=(0,0). We show that these experimental observations are well-captured by the layered t-J-V model, which extends the standard t-J framework to include the long-range Coulomb interaction V and the layered structure. This new perspective elucidates how charge dynamics renormalizes one-particle excitation properties, leading to several profound and often counterintuitive consequences. We demonstrate that the electron dispersion does not exhibit a sharp kink, and Landau quasiparticles persist in the low-energy limit despite a significant suppression of their spectral weight. We further show that while charge fluctuations alone cannot fully account for the pseudogap, they are a crucial component for understanding its formation. Additionally, we reveal that optical plasmon excitations generate fermionic quasiparticles, known as plasmarons, which give rise to a distinct, incoherent replica band. We argue that accurately describing these plasmonic effects requires a three-dimensional theoretical approach. This perspective on plasmon excitations may offer a critically new clue to a long-standing puzzle: why multi-layer cuprate superconductors, containing more than two CuO2 layers per unit cell, consistently exhibit a higher critical temperature Tc than their single-layer counterparts. Finally, we review the spin-fluctuation mechanism of superconductivity suffers from the "self-restraint effect" and show how important the screened Coulomb interaction is in the spin-fluctuation mechanism to realize high-Tc superconductivity.

Figures (35)

• Figure 1: Schematic phase diagram of the high-$T_{c}$ cuprate superconductors. Both hole and electron doping are possible. At half-filling, the system is an antiferromagnetic (AF) Mott insulator. The antiferromagnetism is suppressed by carrier doping, leading to a $d$-wave superconducting ($d$SC) state. On the hole-doped side, the pseudogap phase is realized below the temperature $T^{*}$, where a gaplike feature is observed even above the superconducting onset temperature $T_{c}$. In a wide doping region, an anomalous metallic phase is realized, where the standard Fermi-liquid description does not hold. The actual phase diagram is more complicated as shown in Refs. keimer15 and jjwen19
• Figure 2: Typical charge excitation spectrum along the symmetry axes for $q_z=0$ and $\pi$ computed in the large-$N$ theory of the layered $t$-$J$-$V$ model for electron-doping rate $\delta=0.15$ at zero temperature; the interlayer hopping integral is taken as $t_z=0.1t$. The dotted line denotes the upper boundary of a particle-hole continuum for $q_z=0$. Adapted from Ref. greco16, where the superexchang interaction $J/t=0.3$ and next nearest-neighbor hopping $t'/t=0.3$, and broadening parameter $\Gamma/t=10^{-4}$ were used.
• Figure 3: Plasmon band characterized by a value of $q_{z}$ around ${\bf q}_{\parallel}=(0,0)$. Adapted from Ref. greco16, where the superexchang interaction $J/t=0.3$ and next nearest-neighbor hopping $t'/t=0.3$, and broadening parameter $\Gamma/t=10^{-4}$ were used.
• Figure 4: (a) Plasmon scenario. Intensity map in the plane of $q_{z}$ and $\omega$. The open circles denotes the peak energy, which decreases with increasing $q_{z}$. (b) Incoherent particle-hole scenario. The $q_{z}$ dependence of the peak positions is negligible. (c) Short-range interaction scenario. At small ${\bf q}_{\parallel}=(0.02\pi, 0.02\pi)$, the peak energy increases with $q_{z}$, the opposite dependence to the plasmon scenario (a). (d) Plasmon energy as a function of $t_{z}$ for several choices of $q_{z}$. To define the peak position sharply, a broadening factor $\Gamma$ is taken to be smaller. The gap at $q_{z}=0$ corresponds to the optical plasmon energy. (a), (b), (c) are adapted from Ref. greco19 and (d) from Ref. greco16.
• Figure 5: (a) Imaginary part of the charge susceptibility Im$\chi_c({\bf q},\omega)$ for momentum $(0.02, 0, 0.45)$ (solid black line) computed in the layered $t$-$J$-$V$ model; here $H$, $K$, $L$ are units of $2 \pi /a$, $2 \pi /a$, $2 \pi /c$ with $a$ and $c$ being lattice constants along $x$ ($y$) and $z$ directions, respectively. Superimposed are experimental data (blue symbols), which correspond to the plasmon component in the RIXS raw data. The intensity of Im$\chi_c({\bf q},\omega)$ is scaled to fit the maximum of the RIXS data. (b) Computed intensity map of Im$\chi_c({\bf q},\omega)$ for momenta along the $(H,0,0.45)$ direction. The solid black line corresponds to the maxima of Im$\chi_c({\bf q},\omega)$. The other lines indicate the maxima of Im$\chi_c({\bf q},\omega)$ for different $L$. Experimental plasmon peak positions for momenta along the $(H,0,0.45)$ direction are superimposed as white and gray symbols. The former symbols correspond to peak positions used as an input for the fitting procedure for the $t$-$J$-$V$ model, while the latter were not included. (c) Computed intensity map and maxima for different $H$ along the $(0.05,0,L)$ direction. Experimental data are plotted by open circles. Adapted from Ref. hepting22