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

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.

💡 Research Summary

This review article re‑examines the charge dynamics of high‑temperature cuprate superconductors by emphasizing the role of the long‑range Coulomb interaction (LRC) that goes beyond the on‑site Hubbard repulsion traditionally used in Hubbard and t‑J models. The authors begin by summarising resonant inelastic X‑ray scattering (RIXS) and electron‑energy‑loss spectroscopy (EELS) experiments which reveal a pronounced 1/q² singularity at the in‑plane momentum q∥ = (0,0). This singularity gives rise to an optical plasmon around 1 eV and, in layered cuprates, to an acoustic‑like plasmon branch that disperses strongly with the out‑of‑plane momentum qz.

To capture these observations the authors introduce the layered t‑J‑V model, i.e. the standard t‑J Hamiltonian supplemented by a long‑range Coulomb term V(r) ∝ 1/r and an inter‑layer hopping tz. Using a large‑N expansion they compute the dynamical charge susceptibility χc(q,ω) and the electron self‑energy Σ(k,ω). The theory predicts four key features that have been confirmed experimentally: (i) the acoustic plasmon energy decreases with increasing qz at small in‑plane q∥, opposite to the qz‑independent particle‑hole continuum; (ii) a short‑range‑only model would produce a zero‑sound mode whose energy rises with qz, again contrary to observations; (iii) the acoustic plasmon acquires a gap at q∥ = 0 proportional to tz, explaining the finite energy of the V‑shaped dispersion; (iv) both electron‑ and hole‑doped cuprates display the same acoustic‑plasmon branch.

The impact of these charge excitations on single‑particle properties is profound. The electron dispersion lacks the sharp “kink” traditionally associated with coupling to a bosonic mode; instead, high‑energy renormalisation is dominated by coupling to plasmons and plasmarons. Landau quasiparticles survive at low energies, but their spectral weight is strongly suppressed, consistent with the weak quasiparticle peaks seen in ARPES. The coupling of electrons to the acoustic plasmon generates a distinct incoherent replica band – the plasmaron – which appears as a separate feature in both RIXS and ARPES spectra. Because the plasmon dispersion depends on qz, a fully three‑dimensional treatment is required to describe these effects quantitatively.

A particularly intriguing implication concerns multilayer cuprates (e.g., Y‑based compounds with three CuO₂ planes per unit cell). The acoustic plasmon’s gap scales with tz, so increasing the number of layers enhances inter‑layer hopping, broadens the plasmon band, and strengthens electron‑plasmon coupling. The authors argue that this mechanism naturally explains why multilayer cuprates consistently achieve higher critical temperatures Tc than their single‑layer counterparts.

The review also revisits the spin‑fluctuation mechanism of superconductivity. It points out a “self‑restraint effect” whereby the instantaneous part of the spin‑exchange interaction is partially cancelled by the screened Coulomb interaction, reducing the pairing strength if screening is weak. Conversely, proper screening of the long‑range Coulomb term can reinforce the effective spin‑fluctuation interaction, thereby supporting high‑Tc superconductivity.

Methodologically, the paper combines the large‑N treatment of the t‑J‑V model with Eliashberg theory to obtain self‑consistent solutions for the superconducting gap, quasiparticle renormalisation, and collective charge modes. The authors stress that while the focus is on cuprates, the framework is applicable to other layered correlated electron systems where long‑range Coulomb forces and inter‑layer hopping are relevant.

In summary, by incorporating the long‑range Coulomb interaction into a three‑dimensional layered t‑J‑V model, the authors provide a unified description of charge excitations, plasmon‑induced renormalisation, pseudogap phenomenology, and the enhanced Tc of multilayer cuprates, while also clarifying the interplay between charge and spin fluctuations in the pairing mechanism. This perspective challenges the prevailing short‑range‑only paradigm and opens new avenues for both theoretical and experimental exploration of high‑temperature superconductivity.