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Modern Physics Letters B

Superconductivity in a one-dimensional correlated quantum system

Hanqin Ding, Jun Zhang

Published Jul 12, 2016• 0 citations
Publisher

Abstract

We construct a one-dimensional (1D) theoretical model to clarify the occurrence of superconductivity. The weak-coupling (WC) theory allows a determination of the phase diagram. The constrained hopping induces additional two-body and three-body interactions. At half-filling, the three-body interaction is responsible for the triplet superconducting (TS) correlation. Away from half-filling, the two-body interaction works, favoring the singlet superconducting (SS) correlation. The results are expected to provide an insignificant insight into the superconductivity mechanism.

DOI
10.1142/s0217984916502316

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We study a Hubbard Hamiltonian, including a quite general nearest-neighbor interaction, parametrized by repulsion V, exchange interactions ${J}_{z}{,J}_{\ensuremath{\perp}},$ bond-charge interaction X, and hopping of pairs W. The case of correlated hopping, in which the hopping between nearest neighbors depends upon the occupation of the two sites involved, is also described by the model for sufficiently weak interactions. We study the model in one dimension with usual continuum-limit field theory techniques, and determine the phase diagram. For arbitrary filling, we find a very simple necessary condition for the existence of dominant triplet superconducting correlations at large distance in the spin SU(2) symmetric case: 4V+J<0.4V+J<0.4V+J<0. In the correlated-hopping model, the three-body interaction should be negative for positive V. We also compare the predictions of this weak-coupling treatment with numerical exact results for the correlated-hopping model obtained by diagonalizing small chains and using a Berry phase to determine the opening of the spin gap.
By using the field-theoretical techniques combining bosonization with renormalization group, we study a one-dimensional (1D) model of interacting electrons with on-site repulsion (U > 0), nearest-neighbor (nn) exchange (J) and correlated-hopping (t2, t3) interactions at weak coupling. In the case of a half-filled band, the two-body interaction t2 does not influence phase diagram of the model, while the presence of three-body interaction t3 makes the physics of the system highly non-trivial. By a Hartree–Fock decoupling, the effects of t3 bring about hopping of pairs, V-like (nn Coulomb interaction) and isotropic exchange terms in the reduced model Hamiltonian. Interestingly, a negative t3 provides a possibility for the occurrence of the triplet superconductivity in 1D system with purely repulsive interactions (U, J > 0). The ground state phase diagram including the insulating and superconducting phases is discussed analytically.
At non-half-filling, a one-dimensional interacting electronic model (t–U–R) is studied analytically. The particular correlated hopping keeps particle–hole symmetry of the Hubbard model. Physically, the model involved is equivalent to an extended Hubbard chain incorporating a two-body (X) and a three-body (X˜) site-bond interactions with X˜=2X. The analysis of weak-coupling theory leads to the ground-state phase diagram, which consists of three types of metallic phases, characterized by the charge- (CDW) and spin-density-wave (SDW) and singlet-superconductivity (SS) instabilities.
At half filling, we study analytically a one-dimensional correlated electronic system modeled by an extended Penson–Kolb–Hubbard (PKH) chain with the occupation-dependent hopping. The modification of the electron hopping amplitude is exhibited to induce the additional correlated-hopping interactions. At weak coupling, we use the field theory to obtain ground-state phase diagram, including the SDW, BCDW, BSDW, SS and TS phases for U>0. The induced three-body attractive interaction accounts for the superconductivity absent in the usual PKH model.
At weak coupling and at half filling, we analytically study effects of an intersite three-electron density interaction (P) of the one-dimensional extended Hubbard model in addition to the usual two-electron density interactions (U,V). By the bosonization and renormalization group approaches, we obtain the ground-state phase diagram of the model. In particular, we find that even in the presence of repulsive U and V, the attractive P may give rise to the superconducting phases for 2V≤min{2|P|;4|P|−U}.