Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9911484 · Journal of the Physical Society of Japan

Enhancement of Pairing Correlation and Spin Gap through Suppression of Single-Particle Dispersion in One-Dimensional Models

Masanori Kohno, Masatoshi Imada

Published Jan 1, 2000• 14 citations
arXivHTMLPDF

Abstract

We investigate the effects of suppression of single-particle dispersion near the Fermi level on the spin gap and the singlet-pairing correlation by using the exact diagonalization method for finite-size systems. We consider strongly correlated one-dimensional models, which have flat band dispersions near wave number k=π/2, if the interactions are switched off. Our results for strongly correlated models show that the spin gap region expands as the single-particle dispersion becomes flatter. The region where the singlet-pairing correlation is the most dominant also expands in models with flatter band dispersions. Based on our numerical results, we propose a pairing mechanism induced by the flat-band dispersion.

DOI
10.1143/jpsj.69.25

Related papers

Theoretical study of spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band

Tetsuaki Aida, Karin Matsumoto, Daisuke Ogura +2 more

One promising way to enhance superconductivity is to have coexisting wide and incipient narrow bands, where the Fermi level intersecting the wide band lies just above the narrow band, by which finite-energy spin fluctuations act as glue to mediate pair scattering. As an extreme case of the narrow band dispersion, we investigate spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band. For all of the systems investigated in this study, the Kagome, Lieb, and bilayer square lattices with a flat band, we find that spin-singlet pairing superconductivity is enhanced when the flat band is nearly fully filled, due to the interband pair scattering even when the flat band becomes dispersive by correlation effects. Among these models, enhancement of superconductivity is weak in the Lieb lattice, possibly because the density of states of the wide band goes to zero at the Dirac point where the flat and wide bands intersect. Also, when the electron density is smaller so that the flat band approaches half-filling, ferromagnetic spin fluctuations and spin-triplet pairing arises, which does not develop strongly compared to the case of the spin-singlet pairing for the incipient band situation.

arXiv:2408.10465•Physical review. B./Physical review. B•Aug 19, 2024•7 citations

Pairing and non-Fermi liquid behavior in partially flat-band systems: Beyond nesting physics

Sharareh Sayyad, Edwin W. Huang, Motoharu Kitatani +4 more

While many-body effects in flat-band systems are receiving renewed hot interest in condensed-matter physics for superconducting and topological properties as well as for magnetism, studies have primarily been restricted to multiband systems (with coexisting flat and dispersive bands). Here we focus on one-band systems where a band is ``partially flat,'' comprising flat and dispersive portions in $k$ space to reveal whether intriguing correlation effects can already arise on the simplest possible one-band level. For that, the two-dimensional repulsive Hubbard model is studied for two models having different flat areas in an intermediate-coupling regime with the dynamical mean-field theory combined with the fluctuation exchange approximation. We have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied and this triggers, for the model with a wider flat portion, a triplet-pair superconductivity favored over an unusually wide filling region, which is taken over by a sharply growing singlet pairing. For the model with a narrower flat portion, ${T}_{C}$ against filling exhibits an unusual double-peaked ${T}_{C}$ dome, associated with different numbers of nodes in the gap function having remarkably extended pairs in real space. We identify these as a manifestation of the physics outside the conventional nesting physics where only the pair scattering across the Fermi surface in designated (hot) spots is relevant. Another correlation effect arising from the flattened band is found in a non-Fermi-liquid behavior as detected in the momentum distribution function, frequency dependence of the self-energy, and spectral function. These indicate that unusual correlation physics can indeed occur in flat-band systems.

arXiv:1903.09888•Physical review. B./Physical review. B•Jan 6, 2020•35 citations

Superconductivity from Flat Dispersion Designed in Doped Mott Insulators

Masatoshi Imada, Masanori Kohno

Routes to enhance superconducting instability are explored for doped Mott insulators. With the help of insight for criticalities of metal-insulator transitions, geometrical design of lattice structure is proposed to control the instability. A guideline is to explicitly make flat band dispersions near the Fermi level without suppressing two-particle channels. In a one-dimensional model, numerical studies show that our prescription with finite-ranged hoppings realizes large enhancement of spin-gap and pairing dominant regions. We also propose several multiband systems, where the pairing is driven by intersite Coulomb repulsion.

arXiv:cond-mat/9911185•Physical Review Letters•Jan 3, 2000•106 citations

Effect of dispersion in thefband of the one-dimensional Anderson lattice model

M. Guerrero, Hervé M. Carruzzo

We study the effect of a small dispersion in the f band on the elementary excitations of the one-dimensional Anderson lattice at half filling. We use the density-matrix renormalization-group technique to study the strong-coupling case (large Coulomb repulsion U) and an analytic renormalization-group calculation for weak coupling. When U=0, even a small dispersion in the f band can close the hybridization gap. In contrast, when U is large, the quasiparticle gap remains open and is almost independent of the dispersion in the f band. This means that for a given value of the dispersion, there is a metal-insulator transition for some value of the Coulomb repulsion U. The analytic calculation shows that the transition occurs at U=0. In contrast to the quasiparticle gap, the spin gap is strongly suppressed by the dispersion in the f band. This suppression is associated with the enhancement of antiferromagnetic correlations. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Dec 15, 1996•1 citation

Effect of antiferromagnetic correlation to single-particle excitations in strongly correlated electron systems

Hiroaki Kusunose

An effect of antiferromagnetic fluctuations on single-particle excitations is examined on the basis of an extended dynamical mean-field theory that takes account of long-range spin fluctuations onto the local self energy. We demonstrate that the single-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior near the Fermi energy due to the critical antiferromagnetic fluctuations. We also show that for the symmetric case in the Anderson lattice model, the hybridized-band gap is enlarged by the antiferromagnetic fluctuations. In both models the antiferromagnetic fluctuations suppress the double occupancy of the correlated electrons.

Journal of Physics Conference Series•Mar 1, 2009•0 citations

Spin gaps in two models of strongly correlated electron systems

Arnold E. Sikkema

Two aspects of strongly correlated electron systems are studied in this thesis. Hubbard-type models are thought to be at the basis of high-critical-temperature superconductivity. One interaction which has not had much study is the nearest-neighbour hopping of on-site singlet pairs. We refine earlier renormalization group arguments and, using the density-matrix renormalization group method, numerically confirm their prediction that a spin gap opens at infinitesimal pair-hopping amplitude V > 0 in the one-dimensional tight-binding model. We also find a phase separation transition at a finite V > 0 as well as a spin-gap transition at a finite V < 0. The exotic magnetic behaviour of heavy-fermion materials involves an interplay between the screening of local moments from each other and the formation of a magnetic state of long range order. While the single-impurity Kondo Hamiltonian is thought to model some aspects of this behaviour, the properties of the Kondo lattice model away from half-filling are largely unknown. We determine the presence of a spin-gap region in the phase diagram of the one-dimensional Heisenberg-Kondo lattice model and make predictions about certain concealed dimerization order parameters.

•Jan 1, 2009•0 citations
We investigate the effects of suppression of single-particle dispersion near the Fermi level on the spin gap and the singlet-pairing correlation by using the exact diagonalization method for finite-size systems. We consider strongly correlated one-dimensional models, which have flat band dispersions near wave number k=π/2, if the interactions are switched off. Our results for strongly correlated models show that the spin gap region expands as the single-particle dispersion becomes flatter. The region where the singlet-pairing correlation is the most dominant also expands in models with flatter band dispersions. Based on our numerical results, we propose a pairing mechanism induced by the flat-band dispersion.
One promising way to enhance superconductivity is to have coexisting wide and incipient narrow bands, where the Fermi level intersecting the wide band lies just above the narrow band, by which finite-energy spin fluctuations act as glue to mediate pair scattering. As an extreme case of the narrow band dispersion, we investigate spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band. For all of the systems investigated in this study, the Kagome, Lieb, and bilayer square lattices with a flat band, we find that spin-singlet pairing superconductivity is enhanced when the flat band is nearly fully filled, due to the interband pair scattering even when the flat band becomes dispersive by correlation effects. Among these models, enhancement of superconductivity is weak in the Lieb lattice, possibly because the density of states of the wide band goes to zero at the Dirac point where the flat and wide bands intersect. Also, when the electron density is smaller so that the flat band approaches half-filling, ferromagnetic spin fluctuations and spin-triplet pairing arises, which does not develop strongly compared to the case of the spin-singlet pairing for the incipient band situation.
While many-body effects in flat-band systems are receiving renewed hot interest in condensed-matter physics for superconducting and topological properties as well as for magnetism, studies have primarily been restricted to multiband systems (with coexisting flat and dispersive bands). Here we focus on one-band systems where a band is ``partially flat,'' comprising flat and dispersive portions in kkk space to reveal whether intriguing correlation effects can already arise on the simplest possible one-band level. For that, the two-dimensional repulsive Hubbard model is studied for two models having different flat areas in an intermediate-coupling regime with the dynamical mean-field theory combined with the fluctuation exchange approximation. We have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied and this triggers, for the model with a wider flat portion, a triplet-pair superconductivity favored over an unusually wide filling region, which is taken over by a sharply growing singlet pairing. For the model with a narrower flat portion, TC{T}_{C}TC​ against filling exhibits an unusual double-peaked TC{T}_{C}TC​ dome, associated with different numbers of nodes in the gap function having remarkably extended pairs in real space. We identify these as a manifestation of the physics outside the conventional nesting physics where only the pair scattering across the Fermi surface in designated (hot) spots is relevant. Another correlation effect arising from the flattened band is found in a non-Fermi-liquid behavior as detected in the momentum distribution function, frequency dependence of the self-energy, and spectral function. These indicate that unusual correlation physics can indeed occur in flat-band systems.
Routes to enhance superconducting instability are explored for doped Mott insulators. With the help of insight for criticalities of metal-insulator transitions, geometrical design of lattice structure is proposed to control the instability. A guideline is to explicitly make flat band dispersions near the Fermi level without suppressing two-particle channels. In a one-dimensional model, numerical studies show that our prescription with finite-ranged hoppings realizes large enhancement of spin-gap and pairing dominant regions. We also propose several multiband systems, where the pairing is driven by intersite Coulomb repulsion.
We study the effect of a small dispersion in the f band on the elementary excitations of the one-dimensional Anderson lattice at half filling. We use the density-matrix renormalization-group technique to study the strong-coupling case (large Coulomb repulsion U) and an analytic renormalization-group calculation for weak coupling. When U=0, even a small dispersion in the f band can close the hybridization gap. In contrast, when U is large, the quasiparticle gap remains open and is almost independent of the dispersion in the f band. This means that for a given value of the dispersion, there is a metal-insulator transition for some value of the Coulomb repulsion U. The analytic calculation shows that the transition occurs at U=0. In contrast to the quasiparticle gap, the spin gap is strongly suppressed by the dispersion in the f band. This suppression is associated with the enhancement of antiferromagnetic correlations. \textcopyright{} 1996 The American Physical Society.
An effect of antiferromagnetic fluctuations on single-particle excitations is examined on the basis of an extended dynamical mean-field theory that takes account of long-range spin fluctuations onto the local self energy. We demonstrate that the single-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior near the Fermi energy due to the critical antiferromagnetic fluctuations. We also show that for the symmetric case in the Anderson lattice model, the hybridized-band gap is enlarged by the antiferromagnetic fluctuations. In both models the antiferromagnetic fluctuations suppress the double occupancy of the correlated electrons.
Two aspects of strongly correlated electron systems are studied in this thesis. Hubbard-type models are thought to be at the basis of high-critical-temperature superconductivity. One interaction which has not had much study is the nearest-neighbour hopping of on-site singlet pairs. We refine earlier renormalization group arguments and, using the density-matrix renormalization group method, numerically confirm their prediction that a spin gap opens at infinitesimal pair-hopping amplitude V > 0 in the one-dimensional tight-binding model. We also find a phase separation transition at a finite V > 0 as well as a spin-gap transition at a finite V < 0. The exotic magnetic behaviour of heavy-fermion materials involves an interplay between the screening of local moments from each other and the formation of a magnetic state of long range order. While the single-impurity Kondo Hamiltonian is thought to model some aspects of this behaviour, the properties of the Kondo lattice model away from half-filling are largely unknown. We determine the presence of a spin-gap region in the phase diagram of the one-dimensional Heisenberg-Kondo lattice model and make predictions about certain concealed dimerization order parameters.