$d$-Density Wave (DDW) Scenario Description of the New Hidden Charge Order in Cuprates

TL;DR

This paper demonstrates that a microscopic $d$-density wave model can explain the hidden charge order observed in cuprates, favoring axial over diagonal charge orders and predicting checkerboard patterns in the superconducting state.

Contribution

It provides a microscopic theory showing axial charge order is energetically favored over diagonal order in cuprates, aligning with experimental observations.

Findings

Axial charge order is more energetically favorable than diagonal order.

Checkerboard charge order is preferred over stripe order in the superconducting phase.

The theory reproduces key features of the hidden charge order in cuprates.

Abstract

In this paper, we show that the theory of high $T_c$ superconductivity based on a microscopic model with $d$-density wave (DDW) scenario in the pseudogap phase is able to reproduce some of the most important features of the recent experimentally discovered hidden charge order in several families of Cuprates. In particular, by computing and comparing energies of charge orders of different modulation directions derived from a full microscopic theory with $d$-density wave scenario, the axial charge order $\phi_{X(Y)}$ with wavevector $\mathbf{Q}=(Q_0,0)((0,Q_0))$ is shown to be unambiguously energetically more favorable over the diagonal charge order $\phi_{X\pm Y}$ with wavevector $\mathbf{Q}=(Q_0,\pm Q_0)$ at least in commensurate limit, to be expected also to hold even to more general incommensurate case, in agreement with experiment. The two types of axial charge order $\phi_X$ and $\phi_Y$ are degenerate by symmetry. We find that within the superconducting background, biaxial (checkerboard) charge order is energetically more favorable than uniaxial (stripe) charge order, and therefore checkerboard axial charge order should be the one observed in experiments, assuming a single domain of charge ordered state on each CuO$_2$ plane.