Mottness in High-Temperature Copper-Oxide Superconductors

Abstract

The standard theory of metals, Fermi liquid theory, hinges on the key assumption that although the electrons interact, the low-energy excitation spectrum stands in a one-to-one correspondence with that of a non-interacting system. In the normal state of the copper-oxide high-temperature superconductors, drastic deviations from the Fermi liquid picture obtain, highlighted by a pseudogap, broad spectral features and $T-$ linear resistivity. This article focuses on the series of experiments on the copper-oxide superconductors which reveal that the number of low-energy addition states per electron per spin exceeds unity, in direct violation of the key Fermi liquid tenet. These experiments point to new degrees of freedom, not made out of the elemental excitations, as the key mechanism by which Fermi liquid theory breaks down in the cuprates. A recent theoretical advance which permits an explicit integration of the high energy scale in the standard model for the cuprates reveals the source of the new dynamical degrees of freedom at low energies, a charge 2e bosonic field which has nothing to do with pairing but rather represents the mixing with the high energy scales. We demonstrate explicitly that at half-filling, this new degree of freedom provides a dynamical mechanism for the generation of the charge gap, antiferromagnetism in the insulating phase and explains many of the anomalies in the normal state of the cuprates.

Key Issues essay prepared for Rep. Prog. Phys

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• Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence
• Mottness collapse and statistical quantum criticality
• Cofermion Theory for Pseudogap Phenomena and Superconducting Mechanism of Underdoped Cuprate Superconductors
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• Mottness Collapse and T-linear Resistivity in Cuprate Superconductors
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• Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, grand canonical and canonical ensembles
• States induced in the single-particle spectrum by doping a Mott insulator
• Characteristics of the Mott transition and electronic states of high-temperature cuprate superconductors from the perspective of the Hubbard model
• Towards the Standard Model of Fermi Arcs from a Wilsonian Reduction of the Hubbard Model
• From "Weak" to "Strong" Hole Confinement in a Mott Insulator
• Charge 2e Boson Underlies Two - Fluid Model of the Pseudogap in Cuprate Superconductors
• Optical conductivity due to orbital polarons in systems with orbital degeneracy
• Emergence and spectral-weight transfer of electronic states in the Hubbard ladder
• Charge and current orders in the spin-fermion model with overlapping hot spots
• Mott transition and electronic excitation of the Gutzwiller wavefunction
• Quantitative assessment of the universal thermopower in the Hubbard model
• Nature of Split Hubbard Bands at Low Densities
• Photoemission studies of the near Fermi level spectral weight shifts in FeSe1-xTex superconductor
• Emergence of electronic modes by doping Kondo insulators in the Kondo lattice and periodic Anderson models
• Temperature-driven change in band structure reflecting spin-charge separation of Mott and Kondo insulators
• Separation of magnetic and superconducting behaviour in YBCO6.33 (Tc=8.4 K)
• Spinon and eta-spinon correlation functions
• Non-conservation of Fermionic Degrees of Freedom at Low-energy in Doped Mott Insulators
• U(1) slave-particle study of the finite-temperature doped Hubbard model in one and two dimensions
• Pseudogap with Fermi arcs and Fermi pockets in half-filled twisted transition metal dichalcogenides
• Emergence and evolution of electronic modes with temperature in spin-gapped Mott and Kondo insulators
• Electronic modes induced by spin and charge perturbations in Mott and Kondo insulators