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arXiv:cond-mat/0309036 · Physical review. B, Condensed matter

Repulsion-sustained supercurrent and flux quantization in rings of symmetric Hubbard clusters

Agnese Callegari, Michele Cini, Enrico Perfetto, Gianluca Stefanucci

Published Oct 16, 2003• 3 citations
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Abstract

We test the response to a threading magnetic field of rings of five-site ${C}_{4v}$-symmetric repulsive Hubbard clusters connected by weak intercell links; each five-site unit has the topology of a ${\mathrm{CuO}}_{4}$ cluster and a repulsive interaction is included on every site. In a numerical study of the three-unit ring with eight particles, we take advantage of an exact-diagonalization technique which can be generally applied to many-fermion problems. For O-O hopping we find a superconducting flux quantization (SFQ), but for purely Cu-Cu links bound pair propagation is hindered by symmetry. The results agree with $W=0$ pairing theory.

DOI
10.1103/physrevb.68.153103

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We test the response to a threading magnetic field of rings of five-site C4v{C}_{4v}C4v​-symmetric repulsive Hubbard clusters connected by weak intercell links; each five-site unit has the topology of a CuO4{\mathrm{CuO}}_{4}CuO4​ cluster and a repulsive interaction is included on every site. In a numerical study of the three-unit ring with eight particles, we take advantage of an exact-diagonalization technique which can be generally applied to many-fermion problems. For O-O hopping we find a superconducting flux quantization (SFQ), but for purely Cu-Cu links bound pair propagation is hindered by symmetry. The results agree with W=0W=0W=0 pairing theory.
By means of a novel exact-diagonalization technique, we show that bound pairs propagate between repulsive Hubbard clusters in a superconducting fashion. The size of the matrices that must be handled depends on the number of fermion configurations per spin , which is of the order of the square root of the overall size of the Hilbert space. We use CuO 4 units connected by weak O–O links to model the interplanar coupling and c -axis superconductivity in cuprates. The numerical evidence on Cu 2 O 8 and Cu 3 O 12 prompts the proposal of a new analytic scheme describing the propagation of bound pairs and also the superconducting flux quantization in a 3D geometry.
Charge Conjugation and Pairing in a model Cu5_{5}5​O4_{4}4​ Cluster
Highly-symmetric three-band Hubbard Cu-O clusters have peculiar properties when the hole number is such that they admit W=0 hole pairs. These are two-hole eigenstates of the on-site Hubbard repulsion with eigenvalue 0, get bound by correlation effects when dressed by the interaction with the background, and cause superconducting flux quantization. We study the Cu5_{5}5​O4_{4}4​ cluster by exact diagonalization and show that bound electron pairs of 1^{1}1% B2_{2}2​ symmetry are obtained at an appropriate filling, and quantize flux like the hole pairs. The basic mechanism for pairing in this model is the second-order exchange diagram, and an approximate charge conjugation symmetry holds between electron and hole pairs. Further, the flux quantization property requires that the W=0 pairs of ddd symmetry have sss symmetry couterparts, still with W=0; the former are due to a spin fluctuation, while the latter arise from a charge fluctuation mechanism. The simultaneous existence of both is an essential property of our model and is required for any model of superconducting ddd pairs.
Recently, by exact diagonalisation methods, we reported superconducting pairing and flux quantization in Cu-O Hubbard clusters of up to 21 atoms. The pairing is due to a configuration interaction mechanism driven by symmetry, and arises when the least bound holes have vanishing mutual repulsion ( W =0 pairs). The second-order, spin-flip interaction leads to a net attraction for the singlet and repulsion for the triplet. Here we show that electron bound pairs also exist and show similar flux quantization properties. Then, we extend the theory of pairing to the full plane and to all orders.
The fully symmetric Cu-O clusters with a central Cu have two-hole singlet eigenstates which are not affected by the on-site repulsion. These pairs become bound states if the number of holes in the cluster is appropriate; moreover, the quantization at half-integer values of a magnetic test flux is consistent with a superconducting pattern. To investigate the mechanism of pairing, we study the symmetric clusters with $<~$21 atoms and four holes by exact diagonalization. Further, by the diagrammatic expansion of the ground-state energy and of the scattering amplitude, we obtain the spin-flip diagrams for the effective interaction, which is attractive for singlets and repulsive for triplets. A criterion for pairing in cluster calculations is thereby obtained.
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We solve exactly a generalized Hubbard ring with twisted boundary conditions. The magnitude of the nearest-neighbor hopping depends on the occupations of the sites involved and the term which modifies the number of doubly occupied sites tAB=0{t}_{\mathrm{AB}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0tAB​=0. Although $\ensuremath{\eta}$-pairing states with off-diagonal long-range order are part of the degenerate ground state, the behavior of the energy as a function of the twist rules out superconductivity in this limit. A small tAB{t}_{\mathrm{AB}}tAB​ breaks the degeneracy and for moderate repulsive UUU introduce superconducting correlations which lead to ``anomalous'' flux quantization.