Theoretical Insights into Electronic Nematic Order, Bond-Charge Orders, and Plasmons in Cuprate Superconductors

The parent compound of high-Tc cuprate superconductors is a Mott insulator described by the Heisenberg spin–spin interaction on a square lattice. With carrier doping, the charge degree of freedom becomes active and both spin and charge couple to each other, leading to very rich physics including high-Tc superconductivity. In this article, we focus on the charge degree of freedom and review theoretical insights into the electronic nematic order, bond-charge orders, and plasmons. The low-energy charge dynamics is controlled by the spin–spin interaction J, which generates various bond-charge ordering tendencies including the electronic nematic order. The nematic order is driven by a d-wave Pomeranchuk instability and is pronounced in the underdoped region as well as around van Hove filling in the hole-doped case; the nematic tendency is weak in the electron-doped region. Nematicity consistent with the d-wave Pomeranchuk instability was reported for hole-doped cuprates in various experiments such as inelastic neutron scattering, angle-resolved photoemission spectroscopy, Compton scattering, electronic Raman scattering, and measurements of Nernst coefficients and magnetic torque. Although the t–J and Hubbard models correctly predicted the proximity to the nematic instability in cuprates far before experimental indications were obtained, the full understanding of the charge ordering tendencies in hole-doped cuprates still requires further theoretical studies. In electron-doped cuprates, on the other hand, the d-wave bond-charge excitations around momentum q≈(0.5π,0) explain the resonant X-ray scattering data very well. Plasmon excitations are also present and the agreement between the large-N theory of the t–J model and resonant inelastic X-ray scattering measurements is nearly quantitative in both hole- and electron-doped cuprates. Theoretically, the charge dynamics in cuprates is summarized as a dual structure in energy space: the low-energy region scaled by J, where the nematic and various bond-charge orders are relevant, and the high-energy region typically larger than J, where plasmons are predominant. We hope that the present article serves as a sound basis for further experimental and theoretical studies on the origin of the pseudogap and ultimately the high-Tc mechanism.