Fermi pockets and quantum oscillations of the Hall coefficient in high temperature superconductors

Abstract

Recent quantum oscillation measurements in high temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here we explain the observations with the theory that the alleged normal state exhibits a hidden order, the $d$-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle $\pi /2$, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but also touch upon the consequences if the order were to incommensurate. It is shown that while commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets.

Final version with a correction of a minor typo; 6 pages, 2 figures

References in corpus (28)

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• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• LDA energy bands, low-energy Hamiltonians, t', t'', t_{perp}(k), and J_{perp}
• Magnetic order in the pseudogap phase of high-$T_C$ superconductors
• Electron pockets in the Fermi surface of hole-doped high-Tc superconductors
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• Theory of Low-Temperature Hall Effect in Electron-Doped Cuprates
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• Polarized Neutron Measurement of Magnetic Order in YBa2Cu3O6.45
• Specific heat anomaly in the d-density wave state and emergence of incommensurate orbital antiferromagnetic order
• Incommensurate DDW order

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• Fermi-surface reconstruction by stripe order in cuprate superconductors
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• Quantum Oscillations in Hole-Doped Cuprates
• Magnetic-field-enhanced incommensurate magnetic order in the underdoped high-temperature superconductor YBa(2)Cu(3)O(6.45)
• Normal-state nodal electronic structure in underdoped high-Tc copper oxides
• Multiple Quantum Oscillations in the de Haas van Alphen Spectra of the Underdoped High Temperature Superconductor YBa_2Cu_3O_6.5
• Protected nodal electron pocket from multiple-Q ordering in underdoped high temperature superconductors
• Quantum Phase Transition in the Normal State of High-Tc Cuprates at Optimum Doping
• Fermi surface reconstruction in high-Tc superconductors
• Magnetic quantum oscillations in YBa${}_2$Cu${}_3$O${}_{6.61}$ and YBa${}_2$Cu${}_3$O${}_{6.69}$ in fields of up to 85 T; patching the hole in the roof of the superconducting dome
• Electron-hole asymmetry, Dirac fermions, and quantum magnetoresistance in BaMnBi2
• Evidence for a small hole pocket in the Fermi surface of underdoped YBa2Cu3Oy
• Hartree-Fock Computation of the High-Tc Cuprate Phase Diagram
• Fermi-surface reconstruction in a smectic phase of a high temperature superconductor
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• A synthesis of the phenomenology of the underdoped cuprates
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• Single reconstructed Fermi surface pocket in an underdoped single layer cuprate superconductor
• Competing order, Fermi surface reconstruction, and quantum oscillations in underdoped high temperature superconductors
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• Anomalous Nernst effect from a chiral d-density wave state in underdoped cuprate superconductors
• Key issues in theories of high temperature superconductors
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• The enigma of the pseudogap phase of the cuprate superconductors
• Chemical potential oscillations from a single nodal pocket in the underdoped high-Tc superconductor YBa2Cu3O6+x
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• Resolution of two apparent paradoxes concerning quantum oscillations in underdoped high-$T_c$ superconductors
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• Coherent c-axis transport in the underdoped cuprate superconductor YBCO
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• Evidence for two competing order parameters in underdoped cuprates superconductors from a model analysis of the Fermi-arc effects
• Quantum oscillations in a d-wave vortex liquid
• 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)
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• Quantum oscillations in electron doped high temperature superconductors
• Numerical Studies of Quantum Oscillations in the Superconducting vortex mixed state
• Quasiparticle Nernst effect in the cuprate superconductors from the d-density wave theory of the pseudogap phase
• The Mixed State of a $\pi$-Striped Superconductor
• Cuprates, Manganites, and Cobaltites: Multielectron Approach to the Band Structure
• Quantum-Hall physics and three dimensions
• Effective masses in a strongly anisotropic Fermi liquid
• Near doping-independent pocket area from an antinodal Fermi surface instability in underdoped high temperature superconductors
• Effects of quasiparticle ambipolarity on the Nernst effect in underdoped cuprate superconductors
• Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-$T_{\mathrm{c}}$ superconductors
• Singlet versus triplet particle-hole condensates in quantum oscillations in cuprates
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• Quantum oscillations in $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+\delta }$ from an incommensurate $d$-density wave order
• Magnetic breakdown in ortho-II high-temperature cuprates
• Nematicity as a route to a magnetic field-induced spin density wave order; application to the high temperature cuprates
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