Checkerboard order in vortex cores from pair-density-wave superconductivity

TL;DR

This paper explores how pair-density-wave (PDW) superconductivity induces checkerboard charge-density-wave (CDW) patterns in vortex cores and surrounding rings, providing evidence for PDW order in cuprate pseudogap phases.

Contribution

It demonstrates that PDW order causes specific CDW patterns in vortex cores and rings, linking experimental observations to the presence of PDW in high-field cuprates.

Findings

PDW order appears in d-wave vortex cores, inducing checkerboard CDW.

An additional CDW with twice the period appears outside vortex cores.

NMR-detected CDW at high fields is likely due to PDW emergence.

Abstract

We consider competing pair-density-wave (PDW) and $d$-wave superconducting states in a magnetic field. We show that PDW order appears in the cores of $d$-wave vortices, driving checkerboard charge-density-wave (CDW) order in the vortex cores, which is consistent with experimental observations. Furthermore, we find an additional CDW order that appears on a ring outside the vortex cores. This CDW order varies with a period that is twice that of the checkerboard CDW and it only appears where both PDW and $d$-wave order co-exist. The observation of this additional CDW order would provide strong evidence for PDW order in the pseudogap phase of the cuprates. We further argue that the CDW seen by nuclear magnetic resonance at high fields is due to a PDW state that emerges when a magnetic field is applied.