Orbital Currents in Extended Hubbard Models of High-Tc Cuprate Superconductors (original) (raw)
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Orbital currents in extended Hubbard models of high-T$_c$ cuprates
2008
Motivated by the recent report of broken time-reversal symmetry and zero momentum magnetic scattering in underdoped cuprates, we investigate under which circumstances orbital currents circulating inside a unit cell might be stabilized in extended Hubbard models that explicitly include oxygen orbitals. Using Gutzwiller projected variational wave functions that treat on an equal footing all instabilities, we show that orbital currents indeed develop on finite clusters, and that they are stabilized in the thermodynamic limit if additional interactions, e.g. strong hybridization with apical oxygens, are included in the model.
Numerical studies of the Hubbard model
Nuclear Physics B - Proceedings Supplements, 1991
Numerical studies of the two-dimensional Hubbard model have shown that it exhibits the basic phenomena seen in the cuprate materials. At half-filling one finds an antiferromagnetic Mott-Hubbard groundstate. When it is doped, a pseudogap appears and at low temperature d-wave pairing and striped states are seen. In addition, there is a delicate balance between these various phases. Here we review evidence for this and then discuss what numerical studies tell us about the structure of the interaction which is responsible for pairing in this model. stripes, pseudogap behavior, and d x 2 −y 2 pairing. In addition, the numerical studies have shown how delicately balanced these models are between nearly degenerate phases. Doping away from half-filling can tip the balance from antiferromagnetism to a striped state in which half-filled domain walls separate π-phase-shifted antiferromagnetic regions. Altering the next-near-neighbor hopping t ′ or the strength of U can favor d x 2 −y 2 pairing correlations over stripes. This delicate balance is also seen in the different results obtained using different numerical techniques for the same model. For example, density matrix renormalization group (DMRG) calculations for doped 8-leg t-J ladders find evidence for a striped ground state. [12] However, variational and Green's function Monte Carlo calculations for the doped t-J lattice, pioneered by Sorella and co-workers, [23, 24] find groundstates characterized by d x 2 −y 2 superconducting order with only weak signs of stripes. Similarly, DMRG calculations for doped 6-leg Hubbard ladders [14] find stripes when the ratio of U to the near-neighbor hopping t is greater than 3, while various cluster calculations [27, 30-33] find evidence that antiferromagnetism and d x 2 −y 2 superconductivity compete in this same parameter regime. These techniques represent present day state-of-the-art numerical approaches. The fact that they can give different results may reflect the influence of different boundary conditions or different aspect ratios of the lattices that were studied. The n-leg open boundary conditions in the DMRG calculations can favor stripe formation. Alternately, the cluster lattice sizes and boundary conditions can frustrate stripe formation. It is also possible that these differences reflect subtle numerical biases in the different numerical methods. Nevertheless, these results taken together show that both the striped and the d x 2 −y 2 superconducting phases are nearly degenerate low energy states of the doped system. Determinantal quantum Monte Carlo calculations [21] as well as various cluster calculations show that the underdoped Hubbard model also exhibits pseudogap phenomena. [27-32] The remarkable similarity of this behavior to the range of phenomena observed in the cuprates provides strong evidence that the Hubbard and t-J models indeed contain a significant amount of the essential physics of the problem. [34]
Phase Diagram of a Three-Orbital Model for High-Tc Cuprate Superconductors
Physical Review Letters, 2014
We study the phase diagram of an effective three orbital model of the cuprates using Variational Monte-Carlo calculations (VMC) on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant Anti-ferromagnetism (AFM), d-wave superconductivity (SC), and the Fermi-liquid (FL) are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and inter-site correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductors provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by O.K. Andersen. The results of the calculations are that this phase gives way at lower dopings to an AFM phase and at larger copings to a SC phase followed by a FL phase.
Effective theory of fluctuating orbital currents in high-Tc cuprate superconductors
Physical Review B, 2008
We derive an effective dissipative quantum field theory for fluctuating orbital currents in clean CuO2 sheets of high-Tc cuprates, based on a three-band model. The Coulomb repulsion term between Cu-and O-sites is decoupled in terms of current operators representing horizontal and vertical parts of circulating currents within each CuO2 unit cell of the lattice. The model has ordering of currents at finite temperatures. The dissipative kernel in the model is of the form |ω|/|q|, indicating Landau damping. Applications of the effective theory to other models are also discussed. PACS numbers: 74.20.Rp, 74.50.+r, Constructing an effective description of the longwavelength and low-energy physics of high-T c superconducting cuprates represents a profound and formidable problem in physics. Such a description must be consistent with experimental observations of several anomalous normal state properties of these systems. Varma has recently proposed that quantum critical fluctuations associated with the breakup of a subtle order, involving circulating currents, could induce the observed anomalous normal state properties of high-T c superconductors [1]. Essentially, the associated quantum critical fluctuations are suggested to produce a fluctuation spectrum resulting in a Marginal Fermi Liquid . Recently, such a spectrum has been derived from a conjectured effective field theory of circulating currents . It should, however, be mentioned that a recent numerical evaluation of the current-current correlations in a three-band t − J-model with 24 sites, where doubly occupied sites have been projected out, shows no evidence of the orbital current pattern proposed by Varma [4].
Philosophical Magazine, 2014
We briefly overview the importance of Hubbard and Anderson-lattice models as applied to explanation of high-temperature and heavy-fermion superconductivity. Application of the models during the last two decades provided an explanation of the paired states in correlated fermion systems and thus extended essentially their earlier usage to the description of itinerant magnetism, fluctuating valence, and the metal-insulator transition. In second part, we also present some of the new results concerning the unconventional superconductivity and obtained very recently in our group. A comparison with experiment is also discussed, but the main emphasis is put on rationalization of the superconducting properties of those materials within the real-space pairing mechanism based on either kinetic exchange and/or Kondo-type interaction combined with the electron correlation effects.
Pseudogap transition within the superconducting phase in the three-band Hubbard model
2019
The onset of the pseudogap in high-T_c superconducting cuprates (HTSC) is marked by the T^* line in the doping-temperature phase diagram, which ends at a point p^* at zero temperature within the superconducting dome. There is no general consensus on how the pseudogap manifests itself within the superconducting phase. We use cluster dynamical mean field theory on a three-band Hubbard model for the HTSC to study the superconducting phase at T=0 K, obtained when doping the correlated insulator, for two different sets of band parameters and for several values of U. We observe a first-order transition within the superconducting phase, which we believe, marks the onset of the pseudogap. Further, we also observe that the d-wave node vanishes within the superconducting phase at low values of hole doping, lower than that at which the first-order transition occurs. Various aspects of the results and their implications are discussed.
Unconventional superconductivity on the triangular lattice Hubbard model
Physical Review B, 2013
Using large-scale dynamical cluster quantum Monte Carlo simulations, we explore the unconventional superconductivity in the hole-doped Hubbard model on the triangular lattice. Due to the interplay of electronic correlations, geometric frustration, and Fermi surface topology, we find a doubly degenerate singlet pairing state at an interaction strength close to the bare bandwidth. Such an unconventional superconducting state is mediated by antiferromagnetic spin fluctuations along the Γ-K direction, where the Fermi surface is nested. An exact decomposition of the irreducible particle-particle vertex further confirms the dominant component of the effective pairing interaction comes from the spin channel. Our findings suggest the existence of chiral d + id superconductivity in hole-doped Hubbard triangular lattice in strongly correlated regime, and provide insight to the superconducting phases of the water-intercalated sodium cobaltates NaxCoO2 • yH2O, as well as the organic compounds κ-(ET)2X and Pd(dmit)2.
Phase diagram of a three-orbital model for high-Tc cuprate superconductors
Physical review letters, 2014
We study the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.
Incommensurate charge-density-wave instability in the extended three-band Hubbard model
Physical Review B, 1998
The infinite-U three-band Hubbard model is considered in order to describe the CuO 2 planes of the hightemperature superconducting cuprates. The charge instabilities are investigated when the model is extended with a nearest-neighbor repulsion between holes on copper d and oxygen p orbitals and in the presence of a long-range Coulombic repulsion. It is found that a first-order valence instability line ending with a critical point is present as in the previously investigated model without long-range forces. However, the dominant critical instability is the formation of incommensurate charge-density waves, which always occur before the valenceinstability critical point is reached. An effective singular attraction arises in the proximity of the charge-density wave instability, accounting for both a strong pairing mechanism and for the anomalous normal-state properties.