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.