# Dimensional Crossover of Charge-Density Wave Correlations in the Cuprates

## TL;DR

This paper investigates how magnetic fields influence charge-density wave correlations in cuprates, revealing a transition from short-range, out-of-phase order to long-range, in-phase order driven by disorder and Coulomb interactions.

## Contribution

It introduces a theoretical framework explaining the magnetic field-induced crossover in charge-density wave order in cuprates using large-N analysis and Monte-Carlo simulations.

## Key findings

- Long-range charge-density wave order develops above a critical magnetic field.
- The transition involves a change from out-of-phase to in-phase correlations along the c-axis.
- Results align with experimental observations in YBCO and suggest broader implications for cuprates.

## Abstract

Short-range charge-density wave correlations are ubiquitous in underdoped cuprates. They are largely confined to the copper-oxygen planes and typically oscillate out of phase from one unit cell to the next in the c-direction. Recently, it was found that a considerably longer-range charge-density wave order develops in YBCO above a sharply defined crossover magnetic field. This order is more three-dimensional and is in-phase along the c-axis. Here, we show that such behavior is a consequence of the conflicting ordering tendencies induced by the disorder potential and the Coulomb interaction, where the magnetic field acts to tip the scales from the former to the latter. We base our conclusion on analytic large-N analysis and Monte-Carlo simulations of a non-linear sigma model of competing superconducting and charge-density wave orders. Our results are in agreement with the observed phenomenology in the cuprates, and we discuss their implications to other members of this family, which have not been measured yet at high magnetic fields.