Quantum oscillations in $\mathrm{YBa_{2}Cu_{3}O_{6+\delta}}$ from an incommensurate $d$-density wave order

TL;DR

This paper investigates quantum oscillations in YBa2Cu3O6+δ using a model of incommensurate d-density wave order, explaining observed electron pockets and predicting possible detection of hole pockets at higher magnetic fields.

Contribution

It introduces a novel incommensurate d-density wave model for Fermi surface reconstruction in cuprates, aligning with experimental observations and suggesting future high-field measurements.

Findings

Single electron pocket explains observed oscillations.

Hole pocket of twice the frequency is not observed.

Higher magnetic fields may reveal additional pockets.

Abstract

We consider quantum oscillation experiments in $\mathrm{YBa_{2}Cu_{3}O_{6+\delta}}$ from the perspective of an incommensurate Fermi surface reconstruction using an exact transfer matrix method and the Pichard-Landauer formula for the conductivity. The specific density wave order considered is a period-8 $d$-density wave in which the current density is unidirectionally modulated. The current modulation is also naturally accompanied by a period-4 site charge modulation in the same direction, which is consistent with recent magnetic resonance measurements. In principle Landau theory also allows for a period-4 bond charge modulation, which is not discussed, but should be simple to incorporate in the future. This scenario leads to a natural, but not a unique, explanation of why only oscillations from a single electron pocket is observed, and a hole pocket of roughly twice the frequency as dictated by two-fold commensurate order, and the corresponding Luttinger sum rule, is not observed. However, it is possible that even higher magnetic fields will reveal a hole pocket of half the frequency of the electron pocket or smaller. This may be at the borderline of achievable high field measurements because at least a few complete oscillations have to be clearly resolved.