Disorder effects in a model of competing superconducting and charge-density wave orders in YBa$_2$Cu$_3$O$_{6+x}$

TL;DR

This study models the competition between superconductivity and charge-density wave order in YBa2Cu3O6+x, showing how spatially correlated disorder impacts the structure factor and correlation length, aligning with experimental observations.

Contribution

It introduces a non-linear sigma model to analyze disorder effects on competing orders in cuprates, highlighting the role of disorder correlation length and plane-specific disorder.

Findings

Reducing chain layer disorder correlation length decreases charge-density wave structure factor size.

Disorder in CuO2 planes lowers the temperature of the structure factor peak and its magnitude.

Charge-density wave correlation length decreases more than experimentally observed with disorder.

Abstract

There is evidence for competition between superconductivity and short-range charge-density wave order in a number of cuprate compounds and especially in YBa$_2$Cu$_3$O$_{6+x}$. Here, we use a non-linear sigma model of such competition to study the effects of spatially correlated disorder in the chain layers and delta-correlated disorder in the CuO$_2$ layers. The first is relevant to the oxygen ortho structure and the latter may be induced by electron irradiation. We find that reducing the correlation length of the potential on the chain layers decreases the size of the charge-density wave structure factor but has little effect on its temperature dependence, as observed experimentally. At the same time, the charge-density wave correlation length decreases more than is seen in the experiment. The temperature at which the structure factor peaks coincides with $T_c$ and both decrease when disorder is introduced into the CuO$_2$ planes. Strengthening this disorder reduces the magnitude of the structure factor and eventually turns it into a monotonic function of the temperature. This occurs despite an increase in the local magnitude of the charge-density wave order.