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Journal of Physics A Mathematical and General

One hole in a three-band model of a high-temperature superconductor

Iain B. Styles, M W Long

Published Aug 20, 2003• 3 citations
Publisher

Abstract

We study a three-band effective model of a CuO 2 plane for the simple case of a single hole, with the aim of investigating the nature of the ground state stabilized by the motion of a single hole on the CuO 2 lattice. Our model is derived from, and retains the essential physics of the Anderson lattice model, but is more amenable to further investigation by virtue of the lifting of the spin degeneracy on the copper sites provided by perturbation theory. We use the Lanczos algorithm to numerically solve a series of finite systems which tend to the CuO 2 plane in the thermodynamic limit. Although we only study finite systems, the largest systems are sufficiently large to demonstrate behaviour that is independent of the boundary conditions, and is hence representative of the behaviour in the thermodynamic limit. In order to gain a good understanding of the competing energy scales, we consider only a single hole at T = 0. Our calculations predict that the ground state of the three-band model for a single hole is strongly quantum, dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. There is no evidence for a discontinuity in the occupation number, indicating that the system is not a Fermi liquid. These predictions are in contrast to those of the t – J model, where the hole motion alone predicts Nagaoka ferromagnetism for the planar system, and one must include magnetic exchange terms in order to obtain the experimentally observed low-spin ground state.

DOI
10.1088/0305-4470/36/35/320

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A pure Hubbard model with demonstrable pairing adjacent to the Mott-insulating phase

James Champion, M W Long

Abstract. We introduce a Hubbard model on a particular class of geometries, and consider the effect of doping the highly spin-degenerate Mott-insulating state with a microscopic number of holes in the extreme strong-coupling limit. The geometry is quite general, with pairs of atomic sites at each superlattice vertex, and a highly frustrated inter-atomic connectivity: the one dimensional realization is a chain of edge-sharing tetrahedra. The sole model parameter is the ratio of intrapair to inter-pair hopping matrix elements. If the intra-pair hopping is negligible then introducing a microscopic number of holes results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair hopping is comparable with the inter-pair hopping then the groundstate is low spin with short-ranged spin correlations. We exactly solve the correlated motion of a pair of holes in such a state and find that, in 1-d and 2-d, they form a bound pair on a length scale that increases with diminishing binding energy. This result is pertinent to the long-standing problem of hole-motion in the CuO2 planes of the high-temperature superconductors: we have rigorously shown that, on our frustrated geometry, the holes pair up and a short-ranged low-spin state is generated by hole motion alone. Submitted to: J. Phys. A: Math. Gen. 1.

•Jan 1, 2003•1 citation
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Abstract We present a microscopic model of the high temperature superconductors which provides evidence for non-Fermi liquid behaviour. Starting from the Anderson Lattice model, we derive a three-band model of a CuO2 plane. We show that the popular t-J model is a subset of our model under certain assumptions which we show to be unphysical. We study the three-band model on the CuO chain. Using two exact solutions of the model to provide trial variational states, and comparing these with an exact finite system numerical calculation, we demonstrate that the spin degeneracy is lifted by the hole motion alone. This provides Heisenberg spin correlations for a physical choice of parameters, and the system is found to be a Luttinger liquid. In two dimensions we numerically solve a series of systems which limit to the CuO2 plane. We predict that the CuO2 planes will exhibit a highly quantum ground state dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. These predictions are contrary to those of the t-J model, where the hole motion alone predicts huge spin degeneracy for the linear chain, and Nagaoka ferromagnetism for the planar system. To my family. Acknowledgements In recent years there has been a general trend amongst members of the Birmingham Theory Group towards increasingly humourous acknowledgements, some of which have worked superbly well, others have fallen rather flat. My desire to be placed in the latter category is not high, and so I am going to try to suppress the urge to outdo those who have gone before me, and write a sensible set of acknowledgements punctuated with a little light humour.
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We introduce a Hubbard model on a particular class of geometries, and consider the effect of doping the highly spin-degenerate Mott-insulating state with a microscopic number of holes in the extreme strong-coupling limit. The geometry is quite general, with pairs of atomic sites at each superlattice vertex, and a highly frustrated inter-atomic connectivity: the one-dimensional realization is a chain of edge-sharing tetrahedra. The sole model parameter is the ratio of intra-pair to inter-pair hopping matrix elements. If the intra-pair hopping is negligible then introducing a microscopic number of holes results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair hopping is comparable with the inter-pair hopping then the groundstate is low spin with short-ranged spin correlations. We exactly solve the correlated motion of a pair of holes in such a state and find that, in 1d and 2d, they form a bound pair on a length scale that increases with diminishing binding energy. This result is pertinent to the long-standing problem of hole motion in the CuO 2 planes of the high-temperature superconductors: we have rigorously shown that, on our frustrated geometry, the holes pair up and a short-ranged low-spin state is generated by hole motion alone.
A Hamiltonian for the motion of oxygen holes strongly coupled to the Cu spins in a one-dimensional (1D) Cu-O lattice is solved exactly for all dopings. This Hamiltonian retains the dominant O-hole hopping term, that is, spin-exchange hopping of the hole spin with the intervening Cu spin and neglects the weaker non-spin-exchange hopping term. The excitations naturally separate into two independent quasiparticles: spinons and holons. It is this Hamiltonian that should be taken as the correct zeroth-order Hamiltonian from which perturbation theory should be applied. We show that the spinon spectrum is the spectrum of the 1D antiferromagnet incommensurate with the Cu lattice and the holons are spinless noninteracting fermions in a cosine band. The Cu-Cu spin correlation in the ground state increases linearly with doping from antiferromagnetic (-0.443) at x=0 to ferromagnetic (\ensuremath{\approxeq}0.19) at x=1.
New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.
Abstract. We introduce a Hubbard model on a particular class of geometries, and consider the effect of doping the highly spin-degenerate Mott-insulating state with a microscopic number of holes in the extreme strong-coupling limit. The geometry is quite general, with pairs of atomic sites at each superlattice vertex, and a highly frustrated inter-atomic connectivity: the one dimensional realization is a chain of edge-sharing tetrahedra. The sole model parameter is the ratio of intrapair to inter-pair hopping matrix elements. If the intra-pair hopping is negligible then introducing a microscopic number of holes results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair hopping is comparable with the inter-pair hopping then the groundstate is low spin with short-ranged spin correlations. We exactly solve the correlated motion of a pair of holes in such a state and find that, in 1-d and 2-d, they form a bound pair on a length scale that increases with diminishing binding energy. This result is pertinent to the long-standing problem of hole-motion in the CuO2 planes of the high-temperature superconductors: we have rigorously shown that, on our frustrated geometry, the holes pair up and a short-ranged low-spin state is generated by hole motion alone. Submitted to: J. Phys. A: Math. Gen. 1.