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Register a new userPairing, Pseudogap and Fermi Arcs in Cuprates
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We use Angle Resolved Photoemission Spectroscopy (ARPES) to study the relationship between the pseudogap, pairing and Fermi arcs in cuprates. High quality data measured over a wide range of dopings reveals a consistent picture of Fermiology and pairing in these materials. The pseudogap is due to an ordered state that competes with superconductivity rather then preformed pairs. Pairing does occur below Tpair~150K and significantly above Tc, but well below T* and the doping dependence of this temperature scale is distinct from that of the pseudogap. The d-wave gap is present below Tpair, and its interplay with strong scattering creates artificial Fermi arcs for Tc<T<Tpair. However, above Tpair, the pseudogap exists only at the antipodal region. This leads to presence of real, gapless Fermi arcs close to the node. The length of these arcs remains constant up to T*, where the full Fermi surface is recovered. We demonstrate that these findings resolve a number of seemingly contradictory scenarios.
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The proposed loop-current order in cuprates cannot give the observed pseudogap and the Fermi-arcs because it preserves translation symmetry. A modification to a periodic arrangement of the four possible orientations of the order parameter with a large period of between about 12 to 30 lattice constants is proposed and shown in a simple and controlled calculation to give one-particle spectra with every feature as in the ARPES experiments. The results follow from (1) the currents at the boundaries of the periodic domains with similar topology as the Affleck-Marston flux phase, and (2) the mixing introduced by the boundary currents between the states near the erstwhile Fermi-surface and the ghost Fermi-surfaces which are displaced from it by mini-reciprocal vectors. The proposed idea can be ruled out or verified by high resolution diffraction or imaging experiments. It does not run afoul of the variety of different experiments consistent with the loop-current order as well as the theory of the marginal Fermi-liquid and d-wave superconductivity based on quantum-critical fluctuations of the loop current order.
High-$T_c$ cuprates differ from conventional superconductors in three crucial aspects: the superconducting state descends from a strongly correlated Mott-Hubbard insulator, the order parameter exhibits d-wave symmetry and superconducting fluctuations play an all important role. We formulate a theory of the pseudogap state in the cuprates by taking the advantage of these unusual features. The effective low energy theory within the pseudogap phase is shown to be equivalent to the (anisotropic) quantum electrodynamics in (2+1) space-time dimensions (QED$_3$). The role of Dirac fermions is played by the nodal BdG quasiparticles while the massless gauge field arises through unbinding of quantum vortex-antivortex degrees of freedom. A detailed derivation of this QED$_3$ theory is given and some of its main physical consequences are inferred for the pseudogap state. We focus on the properties of symmetric QED$_3$ and propose that inside the pairing protectorate it assumes the role reminiscent of that played by the Fermi liquid theory in conventional metals.
Unveiling the nature of the pseudogap and its relation to both superconductivity and antiferromagnetic Mott insulators, the pairing mechanism, and a non-Fermi liquid phase is a key issue for understanding high temperature superconductivity in cuprates. A number of experimental results gathered especially in recently years have revealed an unexpected inhomogeneous nature of cuprates at the nanoscale, indicating the fundamental inapplicability of the conventional theories based on homogeneous systems. Here we show a microscopic model of pseudogap and pairing mechanisms on the basis of the consideration of the spin state around a bound hole in a CuO2 plane and the resulting magnetic orders, leading eventually to the spin-Peierls distortion responsible for the Cooper pair formation. The present model fits and accounts for the accumulated experimental findings reported previously for cuprates, including stripe-like electronic order, breaking of the rotational symmetry, and the so-called 1/8 anomaly. We believe that the present model can help to develop a complete theoretical framework applicable to a large family of high-temperature superconductors, including ferropnictides and ferrochalcogenides.
Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of antiferromagnetic (AFM, spin density wave (SDW), or similar charge density wave (CDW)) order parameter, competing with superconductivity. We explicitly demonstrate the evolution from Fermi arcs (on the large Fermi surface) observed in ARPES experiments at relatively high temperatures (when both the amplitude and phase of density waves fluctuate randomly) towards formation of typical small electron and hole pockets, which are apparently observed in de Haas - van Alfen and Hall resistance oscillation experiments at low temperatures (when only the phase of density waves fluctuate, and correlation length of the short-range order is large enough). A qualitative criterion for quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of cyclotron frequency, correlation length of fluctuations and Fermi velocity.
At mean-field level the t-J model shows a phase diagram with close analogies to the phase diagram of hole doped cuprates. An order parameter associated with the flux or $d$ charge-density wave ($d$-CDW) phase competes and coexists with superconductivity at low doping showing characteristics identified with the observed pseudogap in underdoped cuprates. In addition, in the $d$-CDW state the Fermi surface is reconstructed toward pockets with low spectral weight in the outer part, resembling the arcs observed in angle-resolved photoemission spectroscopy experiments. However, the $d$-CDW requires broken translational symmetry, a fact that is not completely accepted. Including self-energy corrections beyond the mean, field we found that the self-energy can be written as two distinct contributions. One of these (called $Sigma_{flux}$) dominates at low energy and originates from the scattering between carriers and $d$-CDW fluctuations in proximity to the $d$-CDW instability. The second contribution (called $Sigma_{Rlambda}$) dominates at large energy and originates from the scattering between charge fluctuations under the constraint of non double occupancy. In this paper it is shown that $Sigma_{flux}$ is responsible for the origin of low-energy features in the spectral function as a pseudogap and Fermi arcs. The obtained doping and temperature dependence of the pseudogap and Fermi arcs is similar to that observed in experiments. At low energy, $Sigma_{R lambda}$ gives an additional contribution to the closure of the pseudogap.
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