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

The parent compound of high-T_c 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-T_c 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-T_c mechanism.