Theoretical perspectives on charge dynamics in high-temperature cuprate superconductors

TL;DR

High-$T_c$ cuprates are doped Mott insulators where charge dynamics, shaped by strong correlations, layered structure, and long-range Coulomb interactions, are essential alongside spin dynamics. Using a layered $t$-$J$-$V$ model treated in a large-$N$ expansion, the authors derive a $6\times6$ bosonic propagator that captures both on-site and bond-charge fluctuations, predicting acousticlike plasmons at ${\bf q}_{\parallel}=(0,0)$ with a $q_z$-dependent gap and multiple bond-charge modes ($d$-bond, $s$-bond, $d$CDW) tied to the exchange interaction $J$. Experiments with RIXS and RXS confirm these plasmonic features and reveal a pronounced $d$-wave bond-charge tendency at ${\bf q}_{\parallel}=(0.5\pi,0)$ in electron-doped cuprates, while hole-doped cuprates show more elusive charge-order signals, likely tied to pseudogap physics; La-based cuprates exhibit stripe-like charge order linked to magnetic fluctuations. Overall, the work provides a unified framework that connects plasmonic charge dynamics and bond-charge order across dopings, clarifying universal aspects while highlighting material-specific differences relevant to pseudogap and stripe phenomena.

Abstract

We review recent theoretical progress on the charge dynamics of doped carriers in high-temperature cuprate superconductors. Advances in this field have clarified that doped charges in cuprates exhibit remarkably rich collective behavior, governed by the combined effects of strong electronic correlations, the intrinsic layered crystal structure, and long-range Coulomb interaction. First, the emergence of acousticlike plasmons has been firmly established through quantitative analyses of resonant inelastic x-ray scattering (RIXS) spectra based on the t-J-V model -- an extension of the conventional t-J model that incorporates the layered crystal structure and the long-range Coulomb interaction V. These acousticlike plasmons arise near the in-plane momentum q=(0,0) and possess characteristic energies far below the well-known ~ 1 eV optical plasmon. This behavior is found to be universal across both hole- and electron-doped cuprates, including multilayer systems. Second, in electron-doped cuprates, a pronounced tendency toward d-wave bond-charge order develops near q=(0.5pi, 0), as revealed by resonant x-ray scattering (RXS) and RIXS. As a result, the charge dynamics acquires a dual structure, in which low-energy bond-charge excitations coexist with relatively high-energy plasmons. Third, analogous signatures of charge-order tendency have also been reported in hole-doped cuprates. However, a direct application of the d-wave bond-charge-order framework fails to account for experimental observations. Similarly, the charge-stripe order in La-based cuprates remains unresolved within existing theoretical approaches. Assuming that mobile carriers behave in a largely universal manner across electron- and hole-doped systems, we discuss a possible scenario that may reconcile these diverse experimental findings.

Figures (10)

• Figure 1: Spectral weight of the density-density correlation function Im$\chi^{c}({\bf q},\omega)$ in the plane of excitation energy $\omega$ and in-plane momentum ${\bf q}_{\parallel}$ along the high-symmetry path $(\pi,\pi)$--$(0,0)$--$(\pi,0)$--$(\pi,\pi)$ for $q_z=0$ and $\pi$. The dotted line marks the upper boundary of the particle-hole continuum for $q_{z}=0$. The spectral intensity of the plasmon mode is much stronger than that of the continuum and is truncated at a value of 8 to enhance the contrast of the background continuum. Adapted from Ref. greco16.
• Figure 2: Spectral weight maps of the bond-charge susceptibilities, (a) $\chi_{d{\rm bond}}$, (b) $\chi_{s{\rm bond}}$, and (c) $\chi_{d{\rm CDW}}$ in the plane of in-plane momentum ${\bf q}_{\parallel}$ and excitation energy $\omega$ along the symmetry axes $(\pi,0)$--$(\pi,\pi)$--$(0,0)$--$(\pi,0)$. The out-of-plane momentum is $q_z=\pi$. Adapted from Ref. bejas17.
• Figure 3: (a) Map of charge excitations around the zone center in NCCO with x=0.15. Although the spectral weight is broad, a V-shaped distribution may be recognized. The feature near $\omega=2$ eV at ${\bf q}_{\parallel}=(0,0)$ corresponds to the charge transfer Mott gap and is irrelevant to the present work. Adapted from Ref. ishii05. (b) The V-shaped dispersion of charge excitation (blue points) near ${\bf q}_{\parallel}=(0,0)$ in NCCO with x=0.147. Note the vertical scale in (b) differ from that in (a). Red and gray points denote magnetic excitations and are outside the scope of this review. Adapted from Ref. wslee14.
• Figure 4: (a) In-plane dispersion of plasmons along the $q_{x}$ ($h$) for several $q_{z}$ ($l$) values. (b) Out-of-plane dispersion along the $q_{z}$ ($l$) for several choices of $q_{x}$ ($h$) values. Blue points correspond to LSCO with x=0.16 and red ones to Bi2201. Solid curves are $t$-$J$-$V$ model calculations using $t/J=0.3$, $t/2=350$ meV, $t'=-0.20 t$ for LSCO and $t'=-0.35t$ for Bi2201; $V_{c}=18.9$ eV (52.5 eV), $\alpha=3.47$ (8.14), and $\Gamma=0.20$ (0.29) for LSCO (Bi2201). The larger values of $V_{c}$ and $\alpha$ in Bi2201 arise mainly from its large interlayer spacing $d$. The upper limit of the interlayer hopping $t_{z}$ is $0.01t$ in LSCO. Adapted from Ref. nag20.
• Figure 5: ${\bf q}$ dependence of static $d$-wave bond-charge susceptibility $\chi_{d{\rm bond}}({\bf q})$ for several temperatures at a fixed doping level of $\delta=0.13$. The enhancement of $\chi_{d{\rm bond}}({\bf q})$ with decreasing temperature signals the development of $d$-wave bond-charge correlations. Adapted from Ref. yamase19.