Physical review. B, Condensed matter

Superconducting phases in the presence of Coulomb interaction: From weak to strong correlations

T. Domański, Karol Izydor Wysokiński

Published Jan 1, 1999• 15 citations

Abstract

We study the evolution of the superconducting phases in a model with competing short-range attractive (W) and on-site repulsive (U) interactions. The influence of the correlations on the phase diagram of $s\ensuremath{-}$ and d-wave superconductors is studied by means of various approximations. The knowledge of the normal state correlation effects allows the tracking of the influence of U on the superconductivity in correlated systems. We have found the qualitatively different response of the superconducting phases in systems with $W<{U}_{\mathrm{cr}},$ when the system ceases to superconduct for large enough U, and in the limit of strong $W>{U}_{\mathrm{cr}},$ when the system remains superconducting for arbitrarily large U.

DOI: 10.1103/physrevb.59.173

Related papers

Superconductivity in strongly correlated systems for local repulsive interactions

Humberto M. Silva, Francisco Dinóla Neto, M. A. R. Griffith +4 more

arXiv:2602.10351Feb 10, 20260 citations

Effect of on-site Coulomb repulsion on superconductivity in the boson-fermion model

T. Domański

arXiv:cond-mat/0209022Physical review. B, Condensed matterOct 10, 200213 citations

Superconductivity in a strongly correlated one-band system

T. Domański, Karol Izydor Wysokiński, R. Ramakumar

Physical review. B, Condensed matterAug 1, 19965 citations

Quantum fluctuations, pseudogap, and the T=0 superfluid density in strongly correlated d -wave superconductors

Igor F. Herbut

arXiv:cond-mat/0403095Physical Review BNov 12, 20046 citations

Antiferromagnetism, charge density wave, and d-wave superconductivity in the $t$-$J$-$U$-$V$ model of correlated electrons: Role of direct Coulomb interactions

Marcin Abram, M. Zegrodnik, Józef Spałek

Jul 19, 20160 citations

Effects of nonlocal interactions on s- and d-wave superconducting correlations in the extended Hubbard model

Pavol Farkašovský

arXiv:2606.20260Jun 18, 20260 citations

Physical review. B, Condensed matter

Superconducting phases in the presence of Coulomb interaction: From weak to strong correlations

T. Domański, Karol Izydor Wysokiński

Published Jan 1, 1999• 15 citations

Publisher

Abstract

s\ensuremath{-}

and d-wave superconductors is studied by means of various approximations. The knowledge of the normal state correlation effects allows the tracking of the influence of U on the superconductivity in correlated systems. We have found the qualitatively different response of the superconducting phases in systems with

W<{U}_{\mathrm{cr}},

when the system ceases to superconduct for large enough U, and in the limit of strong

W>{U}_{\mathrm{cr}},

when the system remains superconducting for arbitrarily large U.

DOI: 10.1103/physrevb.59.173

Related papers

Superconductivity in strongly correlated systems for local repulsive interactions

Humberto M. Silva, Francisco Dinóla Neto, M. A. R. Griffith +4 more

The understanding of the mechanisms responsible for superconductivity in strongly correlated systems is an interesting and important subject in condensed matter physics. Several theoretical proposals were considered for these systems. The Coulomb interaction between electrons allow a new approach to study this problem. In this paper, we use a usual Hubbard model with a local repulsive interaction to describe a 2D system. The system of equations are solved using the Green's functions method, within a Hubbard-I mean field approximation, which allows to treat the strong interaction limit. We consider both cases of attractive and repulsive interactions and obtain the zero temperature phase diagram of the model. Our results show, in the repulsive case, the existence of a superconducting ground state mediated by the kinetic electronic energy and described by a non-local order parameter. A minimum value of the repulsive interaction $U_{min}$ is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature $T_c$ shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.The understanding of the mechanisms responsible for superconductivity in strongly correlated systems is an interesting and important subject in condensed matter physics. Several theoretical proposals were considered for these systems. The Coulomb interaction between electrons allow a new approach to study this problem. In this paper, we use a usual Hubbard model with a local repulsive interaction to describe a 2D system. The system of equations are solved using the Green's functions method, within a Hubbard-I mean field approximation, which allows to treat the strong interaction limit. We consider both cases of attractive and repulsive interactions and obtain the zero temperature phase diagram of the model. Our results show, in the repulsive case, the existence of a superconducting ground state mediated by the kinetic electronic energy and described by a non-local order parameter. A minimum value of the repulsive interaction $U_{min}$ is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature $T_c$ shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.

arXiv:2602.10351Feb 10, 20260 citations

Effect of on-site Coulomb repulsion on superconductivity in the boson-fermion model

T. Domański

We study the influence of the repulsive Coulomb interactions on the thermodynamic properties of the boson-fermion model with an anisotropic $(d$ -wave and extended s-wave) order parameter. Superconductivity is induced in this model from the anisotropic charge exchange interaction between the conduction-band fermions (electrons or holes) and the immobile hard-core bosons (the localized electron pairs). The on-site Coulomb repulsion competes with this pairing interaction and hence is expected to have a detrimental influence on superconductivity. We analyze this effect in some detail, considering the two opposite limits of the weak and strong repulsion. A possible crossover between both these regimes is also discussed.We study the influence of the repulsive Coulomb interactions on the thermodynamic properties of the boson-fermion model with an anisotropic $(d$-wave and extended s-wave) order parameter. Superconductivity is induced in this model from the anisotropic charge exchange interaction between the conduction-band fermions (electrons or holes) and the immobile hard-core bosons (the localized electron pairs). The on-site Coulomb repulsion competes with this pairing interaction and hence is expected to have a detrimental influence on superconductivity. We analyze this effect in some detail, considering the two opposite limits of the weak and strong repulsion. A possible crossover between both these regimes is also discussed.

arXiv:cond-mat/0209022Physical review. B, Condensed matterOct 10, 200213 citations

Superconductivity in a strongly correlated one-band system

T. Domański, Karol Izydor Wysokiński, R. Ramakumar

We study superconductivity in the extended Hubbard model with a strong on-site repulsion U and weak attractive density-density interaction ${\mathit{V}}_{\mathit{ij}}$ . The electron correlation effects, beyond the weak-coupling regime of U, are included approximately by employing Hubbard decoupling approximations. The formulas for superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ of the present approach are compared to those obtained with the strong-coupling expansion and slave-boson techniques. The methods share some common features. We discuss behavior of ${\mathit{T}}_{\mathit{c}}$ for superconducting phases with s- and d-wave symmetry of the superconducting order parameter. In contrast to the mean-field treatment of U, we find that the strong on-site repulsion does not destroy superconductivity induced by ${\mathit{V}}_{\mathit{ij}}$0 even when U\ensuremath{\gg}|${\mathit{V}}_{\mathit{ij}}$|. \textcopyright{} 1996 The American Physical Society.We study superconductivity in the extended Hubbard model with a strong on-site repulsion U and weak attractive density-density interaction ${\mathit{V}}_{\mathit{ij}}$. The electron correlation effects, beyond the weak-coupling regime of U, are included approximately by employing Hubbard decoupling approximations. The formulas for superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ of the present approach are compared to those obtained with the strong-coupling expansion and slave-boson techniques. The methods share some common features. We discuss behavior of ${\mathit{T}}_{\mathit{c}}$ for superconducting phases with s- and d-wave symmetry of the superconducting order parameter. In contrast to the mean-field treatment of U, we find that the strong on-site repulsion does not destroy superconductivity induced by ${\mathit{V}}_{\mathit{ij}}$0 even when U\ensuremath{\gg}|${\mathit{V}}_{\mathit{ij}}$|. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterAug 1, 19965 citations

Quantum fluctuations, pseudogap, and the T=0 superfluid density in strongly correlated d -wave superconductors

Igor F. Herbut

I study the effect of Coulomb interaction on superconducting order in a $d$ -wave lattice superconductor at $T=0$ by considering the superconducting saddle point in the two-dimensional $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model with a repulsion $U$ . The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at $T=0$ has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large $U$ . This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively.I study the effect of Coulomb interaction on superconducting order in a $d$-wave lattice superconductor at $T=0$ by considering the superconducting saddle point in the two-dimensional $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model with a repulsion $U$. The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at $T=0$ has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large $U$. This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively.

arXiv:cond-mat/0403095Physical Review BNov 12, 20046 citations

Antiferromagnetism, charge density wave, and d-wave superconductivity in the $t$ - $J$ - $U$ - $V$ model of correlated electrons: Role of direct Coulomb interactionsAntiferromagnetism, charge density wave, and d-wave superconductivity in the $t$-$J$-$U$-$V$ model of correlated electrons: Role of direct Coulomb interactions

Marcin Abram, M. Zegrodnik, Józef Spałek

We study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the $t$ - $J$ - $U$ - $V$ model of strongly correlated electrons using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term $V$ in stabilizing the CDW phase and show it appears only above some critical values of $V$ and in a limited hole doping range $\delta$ . The effect of the term $V$ on SC and AF phases is that a strong interaction suppresses SC altogether, whereas the AF order is not significantly influenced by its presence. Calculations for the case of pure SC phase have been also carried out within an extended approach, the extended approach, the diagrammatic expansion for the Gutzwiller wave function (DE-GWF) in order to analyze influence of the higher-order correlations onto this phase beyond the renormalized mean field approach. In the Appendices we discuss, the specific ambiguity of the choice of the Gutzwiller renormalization factors within the SGA when either AF or CDW orders are considered.We study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the $t$-$J$-$U$-$V$ model of strongly correlated electrons using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term $V$ in stabilizing the CDW phase and show it appears only above some critical values of $V$ and in a limited hole doping range $\delta$. The effect of the term $V$ on SC and AF phases is that a strong interaction suppresses SC altogether, whereas the AF order is not significantly influenced by its presence. Calculations for the case of pure SC phase have been also carried out within an extended approach, the extended approach, the diagrammatic expansion for the Gutzwiller wave function (DE-GWF) in order to analyze influence of the higher-order correlations onto this phase beyond the renormalized mean field approach. In the Appendices we discuss, the specific ambiguity of the choice of the Gutzwiller renormalization factors within the SGA when either AF or CDW orders are considered.

Jul 19, 20160 citations

Effects of nonlocal interactions on s- and d-wave superconducting correlations in the extended Hubbard model

Pavol Farkašovský

We investigate the influence of nonlocal interactions on superconducting correlations within the extended Hubbard model. In addition to the on-site Coulomb interaction and nearest-neighbor hopping, we include next-nearest-neighbor hopping together with several physically relevant nonlocal terms, namely nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction, and pair hopping. Using Lanczos exact diagonalization on a $4\times4$ cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s- and d-wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d-wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s-wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.We investigate the influence of nonlocal interactions on superconducting correlations within the extended Hubbard model. In addition to the on-site Coulomb interaction and nearest-neighbor hopping, we include next-nearest-neighbor hopping together with several physically relevant nonlocal terms, namely nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction, and pair hopping. Using Lanczos exact diagonalization on a $4\times4$ cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s- and d-wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d-wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s-wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.

arXiv:2606.20260Jun 18, 20260 citations

s\ensuremath{-}

W<{U}_{\mathrm{cr}},

when the system ceases to superconduct for large enough U, and in the limit of strong

W>{U}_{\mathrm{cr}},

when the system remains superconducting for arbitrarily large U.

U_{min}

is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature

T_c

shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.

We study the influence of the repulsive Coulomb interactions on the thermodynamic properties of the boson-fermion model with an anisotropic

(d

-wave and extended s-wave) order parameter. Superconductivity is induced in this model from the anisotropic charge exchange interaction between the conduction-band fermions (electrons or holes) and the immobile hard-core bosons (the localized electron pairs). The on-site Coulomb repulsion competes with this pairing interaction and hence is expected to have a detrimental influence on superconductivity. We analyze this effect in some detail, considering the two opposite limits of the weak and strong repulsion. A possible crossover between both these regimes is also discussed.

We study superconductivity in the extended Hubbard model with a strong on-site repulsion U and weak attractive density-density interaction

{\mathit{V}}_{\mathit{ij}}

. The electron correlation effects, beyond the weak-coupling regime of U, are included approximately by employing Hubbard decoupling approximations. The formulas for superconducting transition temperature

{\mathit{T}}_{\mathit{c}}

of the present approach are compared to those obtained with the strong-coupling expansion and slave-boson techniques. The methods share some common features. We discuss behavior of

{\mathit{T}}_{\mathit{c}}

for superconducting phases with s- and d-wave symmetry of the superconducting order parameter. In contrast to the mean-field treatment of U, we find that the strong on-site repulsion does not destroy superconductivity induced by ${\mathit{V}}_{\mathit{ij}}$0 even when U\ensuremath{\gg}|${\mathit{V}}_{\mathit{ij}}$|. \textcopyright{} 1996 The American Physical Society.

I study the effect of Coulomb interaction on superconducting order in a

d

-wave lattice superconductor at

T=0

by considering the superconducting saddle point in the two-dimensional $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model with a repulsion

U

. The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at

T=0

has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large

U

. This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively.

Antiferromagnetism, charge density wave, and d-wave superconductivity in the

t

J

U

V

model of correlated electrons: Role of direct Coulomb interactions

We study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the

t

J

U

V

model of strongly correlated electrons using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term

V

in stabilizing the CDW phase and show it appears only above some critical values of

V

and in a limited hole doping range

\delta

. The effect of the term

V

on SC and AF phases is that a strong interaction suppresses SC altogether, whereas the AF order is not significantly influenced by its presence. Calculations for the case of pure SC phase have been also carried out within an extended approach, the extended approach, the diagrammatic expansion for the Gutzwiller wave function (DE-GWF) in order to analyze influence of the higher-order correlations onto this phase beyond the renormalized mean field approach. In the Appendices we discuss, the specific ambiguity of the choice of the Gutzwiller renormalization factors within the SGA when either AF or CDW orders are considered.

4\times4

cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s- and d-wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d-wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s-wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.