Mean-Field Analysis of Intra-Unit-Cell Order in the Emery Model of the CuO$_2$ Plane

TL;DR

This paper uses mean-field analysis of the Emery model to explore intra-unit-cell orders in cuprate superconductors, revealing how interactions influence nematic, nematic-spin-nematic, and loop-current phases.

Contribution

It provides a microscopic understanding of intra-unit-cell orders in the Emery model, showing how interactions favor or suppress specific phases and their coexistence.

Findings

Nematic and nematic-spin-nematic orders are driven by O-O interactions.

Loop-current order can coexist with nematic order.

Interactions modulate the stability of intra-unit-cell phases.

Abstract

Motivated by recent experiments on high-$T_c$ cuprate superconductors pointing towards intra-unit-cell order in the pseudogap phase, we investigate three distinct intra-unit-cell-ordering possibilities: nematic, nematic-spin-nematic, and current-loop order. The first two are Fermi-surface instabilities involving a spontaneous charge and magnetization imbalance between the two oxygen sites in the unit cell, respectively, while the third describes circulating currents within the unit cell. We analyze the three-band Emery model of a single CuO$_2$ layer including various on-site and nearest-neighbor interactions within a self-consistent mean-field approach. We show how these on-site and further-neighbor repulsions suppress or enhance particular IUC orders. In particular, we show that the attractive interactions necessary for nematic and nematic-spin-nematic orders in one-band models have their natural microscopic origin in the O-O on-site and nearest-neighbor repulsions in the three-band model. Finally, we find that while the nematic and nematic-spin-nematic orders cannot coexist in this framework, the loop-current order can coexist with nematic order.