Resolution of two apparent paradoxes concerning quantum oscillations in underdoped high-$T_c$ superconductors

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.

Accepted version, Phys. Rev. B, brief clarifying comments and updated references

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• Fermi Surface and Pseudogap Evolution in a Cuprate Superconductor
• Magnetic Breakdown in the electron-doped cuprate superconductor Nd${}_{2-x}$Ce${}_x$CuO${}_4$: the reconstructed Fermi surface survives in the strongly overdoped regime
• Fermi Surface of the Electron-doped Cuprate Superconductor Nd_{2-x}Ce_xCuO_{4} Probed by High-Field Magnetotransport
• Key issues in theories of high temperature superconductors
• Multiple quantum oscillation frequencies in $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+\delta }$ and bilayer splitting
• Reconsidering the interpretation of quantum oscillation experiments on underdoped YBa(2)Cu(3)O(6+x)
• Quantum oscillations in electron doped high temperature superconductors
• Quasiparticle Nernst effect in the cuprate superconductors from the d-density wave theory of the pseudogap phase
• Quantum oscillations in $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+\delta }$ from an incommensurate $d$-density wave order
• Singlet versus triplet particle-hole condensates in quantum oscillations in cuprates
• Magnetic breakdown and quantum oscillations in electron-doped high temperature superconductor $\mathrm{N}{\mathrm{d}}_{2-\mathrm{x}}\mathrm{C}{\mathrm{e}}_{\mathrm{x}}\mathrm{Cu}{\mathrm{O}}_4$
• Gutzwiller-projected wave functions for the pseudogap state of underdoped high-temperature superconductors
• Density Wave States in the Presence of an External Magnetic Field
• Theoretical investigation of pseudo-gap state of YBCO
• Investigation of chiral density wave mean field Hamiltonian