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Springer eBooks

Impurity Effects on the Superconducting State with a Nodeless Gap in the t-J Model

Hiroki Tsuchiura, Yukio Tanaka, Masao Ogata, Satoshi Kaskeava

Published Jan 1, 1999• 0 citations
Publisher
DOI
10.1007/978-4-431-66874-9_74

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Extended t-t'-t"-J-U models in which the second-nearest-neighbor hopping (t') and third-nearest-neighbor hopping (t") are included are studied using renormalized mean field theory. The models are meant to be low-energy effective models for the Hubbard models, and hence the Heisenberg exchange integral J and Hubbard repulsion U are related by J = 4t(2)/U. The trial wavefunctions for the ground states are partially Gutzwiller projected Hartree-Fock states. The Gutzwiller projection is implemented by means of a Gutzwiller approximation, and the site double occupancy d is taken as a variational parameter. It is found that a large |t'/t| narrows the band filling range that sustains antiferromagnetism (AFM) in the ground state, enhances the d-wave singlet superconductivity (dSC) in hole overdoped systems, but suppresses the dSC in electron overdoped systems. For a system that has large |t'/t| and |t"/t'|, the superconductivity (SC) at the onset of AFM in hole doped band filling is strongly suppressed. On the excitation occurring, when an electron doped system simultaneously contains SC and AFM, the system is found to have a nodeless gap at the Fermi level. Finally, the result of this study is related to experiments on the superconducting cuprates.

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R. Zeyher, A. Greco

Zeitschrift für Physik B Condensed Matter•Dec 1, 1997•9 citations
The Anderson impurity model (AIM) has long served as a cornerstone in the study of correlated electron systems. While numerical renormalization group (RG) offers great flexibility for metallic reservoirs, it becomes impossible in an unbiased way when a spectral gap $\mathrm{\ensuremath{\Delta}}$ opens up in the tunneling density of states. The only known exception is provided by the superconducting bath. In this paper, we lift these limitations by developing a numerical RG procedure that employs a discretization of the gapped tunneling densities of states into patches that accumulate at the gap edges. This reveals an unusual double scaling, which is a shared behavior between the superconducting and the scalar gapped AIMs. Moreover, it requires a special iterative diagonalization procedure with an alternating scheme for discarding states only every second iteration. The discretization and the diagonalization scheme form together what we refer to as the log-gap numerical RG. It is successfully applied to the superconducting and to the scalar gapped AIM. Consequently, it reveals that both models belong to the same RG equivalence class, which manifests physically in common singlet-doublet quantum phase transitions accompanied by in-gap bound states of given parities. While superconducting AIM is mainly used for benchmarking the log-gap numerical RG, we also rigorously confirm the phenomenon of in-gap states escaping into the continuum. The gapped AIM is then tackled in an exact numerical RG approach and confirms quantitatively the assertions based on models with auxiliary metallic leads, but reveals that the other common approach used, for example, in the work of Moca and Roman [Phys. Rev. B 81, 235106 (2010)] is of strictly approximate nature.
The competition between bulk color superconductivity and the localized screening of a heavy quark impurity, analogous to the Kondo effect, leads to a rich spectrum of phenomena in dense quark matter. We investigate this competition at the edge of a superconducting quark bulk, where both the superconducting gap and the Kondo scale are dynamically generated in a tractable toy model. Utilizing the exact Bethe Ansatz method, we elucidate the resulting boundary physics. We identify distinct regimes characterized by either multiparticle Kondo screening or an unscreened local moment. Crucially, we also uncover a novel intermediate phase featuring impurity screening through a single-particle bound state formed within the superconducting gap. The toy model presented in this work highlights the complex interplay between dynamically generated bulk properties and boundary impurities in extreme quantum chromodynamics environments, offering potential insights into phenomena occurring in heavy-ion collisions and compact stars.
Extended t-t'-t"-J-U models in which the second-nearest-neighbor hopping (t') and third-nearest-neighbor hopping (t") are included are studied using renormalized mean field theory. The models are meant to be low-energy effective models for the Hubbard models, and hence the Heisenberg exchange integral J and Hubbard repulsion U are related by J = 4t(2)/U. The trial wavefunctions for the ground states are partially Gutzwiller projected Hartree-Fock states. The Gutzwiller projection is implemented by means of a Gutzwiller approximation, and the site double occupancy d is taken as a variational parameter. It is found that a large |t'/t| narrows the band filling range that sustains antiferromagnetism (AFM) in the ground state, enhances the d-wave singlet superconductivity (dSC) in hole overdoped systems, but suppresses the dSC in electron overdoped systems. For a system that has large |t'/t| and |t"/t'|, the superconductivity (SC) at the onset of AFM in hole doped band filling is strongly suppressed. On the excitation occurring, when an electron doped system simultaneously contains SC and AFM, the system is found to have a nodeless gap at the Fermi level. Finally, the result of this study is related to experiments on the superconducting cuprates.