arXiv:cond-mat/0201058

Reexamination of d-wave superconductivity in the two-dimensional Hubbard model

Takao Morinari

Published Jan 5, 2002• 0 citations

Abstract

We reexamine the possibility of d-wave superconductivity in the hole-doped two-dimensional Hubbard model. In terms of the gauge field description of the spin fluctuations, we show that d-wave superconductivity is unstable in the perturbative region with respect to the on-site Coulomb repulsion, U. Whereas in the region where d-wave superconductivity is possible, there is a strong constraint on the gap of superconductivity. Analysis of the localized spin moments suggests that there is another d-wave (d_{x^2-y^2}-wave) pairing due to the short-range antiferromagnetic correlation.

DOI: 10.48550/arxiv.cond-mat/0201058

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arXiv:cond-mat/0201058

Reexamination of d-wave superconductivity in the two-dimensional Hubbard model

Takao Morinari

Published Jan 5, 2002• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/0201058

Related papers

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Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range $d$ -wave pair field term, which precipitates a superconducting state in the $d$ -wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the $d$ -wave pair/spin/charge-density matrices. The calculations show a $d$ -wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion $U$ and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. We also demonstrate that negative ${t}^{\ensuremath{'}}$ plays an important role in facilitating $d$ -wave superconductivity.Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range $d$-wave pair field term, which precipitates a superconducting state in the $d$-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the $d$-wave pair/spin/charge-density matrices. The calculations show a $d$-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion $U$ and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. We also demonstrate that negative ${t}^{\ensuremath{'}}$ plays an important role in facilitating $d$-wave superconductivity.

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d

-wave pair field term, which precipitates a superconducting state in the

d

-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the

d

-wave pair/spin/charge-density matrices. The calculations show a

d

-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion

U

and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. We also demonstrate that negative ${t}^{\ensuremath{'}}$ plays an important role in facilitating

d

-wave superconductivity.

d

-wave channel. Extended

s

-wave superconductivity is less likely to occur within this purely electronic model, at least in the physically interesting region of doping.

Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of

d

-wave pairing when a nearest-neighbor Coulomb repulsion

V

is present in addition to the on-site Coulomb repulsion

U

. We find that

d

-wave pairing and the superconducting transition temperature

{T}_{c}

are only weakly suppressed as long as

V

does not exceed

U/2

. This stability is traced to the strongly retarded nature of pairing that allows the

d

-wave pairs to minimize the repulsive effect of

V

. When

V

approaches

U/2

, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of

d

-wave pairing and

{T}_{c}

than for smaller

V

Using the variational Monte Carlo method, we find that a relatively weak long-range electron-phonon interaction induces a

d

-wave superconducting state in doped Mott-Hubbard insulators and/or strongly correlated metals with a condensation energy significantly larger than can be obtained with Coulomb repulsion only. Moreover, the superconductivity is shown to exist for infinite on-site Coulomb repulsion without the need for additional mechanisms such as spin fluctuations to mediate

d

-wave superconductivity. We argue that our superconducting state is robust with respect to a more intricate choice of the trial-wave function and that a possible origin of high-temperature superconductivity lies in a proper combination of strong electron-electron correlations with poorly screened Fr\"ohlich electron-phonon interaction.

d

-wave symmetry turns out to be restricted to densities where the Fermi surface crosses the magnetic zone boundary. A concomitant peak in the magnetic structure factor at $(\ensuremath{\pi},\ensuremath{\pi})$ clearly points to a magnetic mechanism.