From stripe to checkerboard order on the square lattice in the presence of quenched disorder

TL;DR

This paper investigates how quenched disorder influences charge density wave (CDW) order on a square lattice, revealing effects on unidirectionality, domain formation, and local density of states, with implications for cuprate superconductors.

Contribution

It introduces a model showing how quenched disorder affects CDW order, especially the transition between stripe and checkerboard patterns, and proposes analysis techniques for STM data.

Findings

Disorder can restore rotational symmetry by forming 90-degree domains.

Correlation length of Ising order can exceed CDW correlation length.

Disorder induces short-range spatial anisotropies in checkerboard CDW.

Abstract

We discuss the effects of quenched disorder on a model of charge density wave (CDW) ordering on the square lattice. Our model may be applicable to the cuprate superconductors, where a random electrostatic potential exists in the CuO2 planes as a result of the presence of charged dopants. We argue that the presence of a random potential can affect the unidirectionality of the CDW order, characterized by an Ising order parameter. Coupling to a unidirectional CDW, the random potential can lead to the formation of domains with 90 degree relative orientation, thus tending to restore the rotational symmetry of the underlying lattice. We find that the correlation length of the Ising order can be significantly larger than the CDW correlation length. For a checkerboard CDW on the other hand, disorder generates spatial anisotropies on short length scales and thus some degree of unidirectionality. We quantify these disorder effects and suggest new techniques for analyzing the local density of states (LDOS) data measured in scanning tunneling microscopy experiments.