Resolution of two apparent paradoxes concerning quantum oscillations in underdoped high-$T_{c}$ superconductors

TL;DR

This paper resolves two paradoxes in quantum oscillation experiments on underdoped high-$T_c$ superconductors by analyzing ARPES spectral functions and disorder effects, suggesting the absence of hole pockets is due to disorder and vortex scattering.

Contribution

It provides a theoretical resolution to the paradoxes using commensurate $d$-density wave theory, including disorder and vortex scattering effects on Fermi surface signatures.

Findings

Disorder reduces ARPES visibility of electron pockets, mimicking Fermi arcs.

Vortex scattering suppresses the hole pocket frequency in quantum oscillations.

Higher magnetic fields and cleaner samples are needed to detect hole pockets.

Abstract

Recent quantum oscillation experiments in underdoped high temperature superconductors seem to imply two paradoxes. The first paradox concerns the apparent non-existence of the signature of the electron pockets in angle resolved photoemission spectroscopy (ARPES). The second paradox is a clear signature of a small electron pocket in quantum oscillation experiments, but no evidence as yet of the corresponding hole pockets of approximately double the frequency of the electron pocket. This hole pockets should be present if the Fermi surface reconstruction is due to a commensurate density wave, assuming that Luttinger sum rule relating the area of the pockets and the total number of charge carriers holds. Here we provide possible resolutions of these apparent paradoxes from the commensurate $d$-density wave theory. To address the first paradox we have computed the ARPES spectral function subject to correlated disorder, natural to a class of experiments relevant to the materials studied in quantum oscillations. The intensity of the spectral function is significantly reduced for the electron pockets for an intermediate range of disorder correlation length, and typically less than half the hole pocket is visible, mimicking Fermi arcs. Next we show from an exact transfer matrix calculation of the Shubnikov-de Haas oscillation that the usual disorder affects the electron pocket more significantly than the hole pocket. However, when, in addition, the scattering from vortices in the mixed state is included, it wipes out the frequency corresponding to the hole pocket. Thus, if we are correct, it will be necessary to do measurements at higher magnetic fields and even higher quality samples to recover the hole pocket frequency.