Journal of the Physical Society of Japan

Superconductivity Due to Interband Attraction: Competition between Diagonal and Off-Diagonal Long-Range Orders

Kazuhiko Kuroki, Hideo Aoki, Yasutami Takada

Published Apr 15, 1992• 4 citations

Abstract

The phase diagram for spin 1/2 fermions with attractive interband interactions (- V ) is obtained for the two-band Hubbard model in the space of - V , intraband repulsion ( U ), and the band filling from the quantum Monte Carlo calculation along with the mean-field theory in one dimension. The competition of an off-diagonal long-range order with diagonal orders (CDW and SDW) is shown to result in a superconducting ground state arising from interband pairing (i) in the presence of U of right magnitude ( ∼ V ) and (ii) in non-half-filled bands.

DOI: 10.1143/jpsj.61.1161

Related papers

Superconductivity in a repulsively interacting two-band Fermi gas

Kazuhiko Kuroki, Hideo Aoki

Physical Review LettersMay 2, 199418 citations

Superconducting ground state in a model with bond-charge interaction

Marco Airoldi, Alberto Parola

Physical review. B, Condensed matterJun 1, 199519 citations

d-Wave pair density wave superconductivity in a two-orbital model

Samuel Vadnais, Arun Paramekanti

arXiv:2604.07511Apr 8, 20260 citations

Detection of pairing correlation in the two-dimensional Hubbard model

Kazuhiko Kuroki, Hideo Aoki, Takashi Hotta +1 more

arXiv:cond-mat/9606143Physical review. B, Condensed matterFeb 1, 199710 citations

Phase diagram of the extended Hubbard model with pair hopping interaction

G. I. Japaridze, Sarkar, S.

Jan 1, 200217 citations

Antiferromagnetism, Superconductivity and Phase Diagram in the Two-Dimensional Hubbard Model —Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model III—

Takashi Yanagisawa

arXiv:1903.09368Journal of the Physical Society of JapanApr 5, 201913 citations

Journal of the Physical Society of Japan

Superconductivity Due to Interband Attraction: Competition between Diagonal and Off-Diagonal Long-Range Orders

Kazuhiko Kuroki, Hideo Aoki, Yasutami Takada

Published Apr 15, 1992• 4 citations

Publisher

Abstract

DOI: 10.1143/jpsj.61.1161

Related papers

Superconductivity in a repulsively interacting two-band Fermi gas

Kazuhiko Kuroki, Hideo Aoki

Phase diagram of the two-band Fermi gas with repulsive intraband and interband interactions is obtained with the bosonization technique. In the forward-scattering model, there is a region for the superconductivity (SC) within a band due to charge fluctuations in the accompanying band. When the backward scattering is relevant the SC region becomes wider, while when the umklapp scattering is relevant the system is renormalized into two independent single bands, which is considered to cover the regime where superconductivity a\ifmmode\acute\else\textasciiacute\fi{} la single-band attractive Hubbard model is found from quantum Monte Carlo results in the multiband model on discrete lattices.Phase diagram of the two-band Fermi gas with repulsive intraband and interband interactions is obtained with the bosonization technique. In the forward-scattering model, there is a region for the superconductivity (SC) within a band due to charge fluctuations in the accompanying band. When the backward scattering is relevant the SC region becomes wider, while when the umklapp scattering is relevant the system is renormalized into two independent single bands, which is considered to cover the regime where superconductivity a\ifmmode\acute\else\textasciiacute\fi{} la single-band attractive Hubbard model is found from quantum Monte Carlo results in the multiband model on discrete lattices.

Physical Review LettersMay 2, 199418 citations

Superconducting ground state in a model with bond-charge interaction

Marco Airoldi, Alberto Parola

An electronic Hubbard-type model with bond-charge interaction and on-site repulsion U is studied in one and two dimensions. Evidence is provided in favor of superconductivity, without phase separation, for U ${\mathit{U}}_{\mathit{c}}$ (n), although no explicit attraction between particles is present in the Hamiltonian. The presence of a bound state for two particles in vacuum in D=1 and 2 (but not for D=3) suggests that, at low density and low dimensionality, superconductivity is due to condensation of preexistent pairs (dimers). The one-dimensional (1D) phase diagram is studied analytically as well as numerically and shows a transiiton between a Luttinger liquid and a strong-coupling phase with diverging superconducting susceptibility. Estimates of critical exponents are given at low density and at quarter filling for several values of the parameters. The 2D model at quarter filling is analyzed by Lanczos diagonalization on a 4\ifmmode\times\else\texttimes\fi{}4 cluster. The numerical results are consistent with the phase diagram obtained by BCS mean-field theory and is qualitatively similar to the 1D case: a ground state with spin gap and off-diagonal long-range order at U ${\mathit{U}}_{\mathit{c}}$ (n); and a Fermi liquid above ${\mathit{U}}_{\mathit{c}}$ with no sign of phase separation.An electronic Hubbard-type model with bond-charge interaction and on-site repulsion U is studied in one and two dimensions. Evidence is provided in favor of superconductivity, without phase separation, for U${\mathit{U}}_{\mathit{c}}$(n), although no explicit attraction between particles is present in the Hamiltonian. The presence of a bound state for two particles in vacuum in D=1 and 2 (but not for D=3) suggests that, at low density and low dimensionality, superconductivity is due to condensation of preexistent pairs (dimers). The one-dimensional (1D) phase diagram is studied analytically as well as numerically and shows a transiiton between a Luttinger liquid and a strong-coupling phase with diverging superconducting susceptibility. Estimates of critical exponents are given at low density and at quarter filling for several values of the parameters. The 2D model at quarter filling is analyzed by Lanczos diagonalization on a 4\ifmmode\times\else\texttimes\fi{}4 cluster. The numerical results are consistent with the phase diagram obtained by BCS mean-field theory and is qualitatively similar to the 1D case: a ground state with spin gap and off-diagonal long-range order at U${\mathit{U}}_{\mathit{c}}$(n); and a Fermi liquid above ${\mathit{U}}_{\mathit{c}}$ with no sign of phase separation.

Physical review. B, Condensed matterJun 1, 199519 citations

d-Wave pair density wave superconductivity in a two-orbital model

Samuel Vadnais, Arun Paramekanti

Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing ( $p_x,p_y$ ) or ( $d_{xz}, d_{yz})$ orbitals on the square lattice. For minimal interorbital $t$ - $J$ or $t$ - $V$ on-site interactions, a random phase approximation uncovers regimes of instability towards incommensurate $d_{xy}$ pair density wave ( $d$ -PDW) superconductivity with driven by interband pairing. We study the competition of PDW order with uniform nodal $d_{xy}$ pairing states and magnetic and charge density wave (CDW) instabilities. At strong coupling, we derive an effective hard-core Cooper pair Hamiltonian which we study using a bosonic Gutzwiller ansatz to reveal a period- $2$ PDW over a wide range of fillings as well as a checkerboard CDW at quarter-filling. Our results apply to correlated multi-orbital materials with quasi-1D bands, Hubbard models on the square-octagon lattice, and atomic fermions in $p$ -orbitals. Our work highlights the role of the orbital content and multiband Fermi surfaces in stabilizing interband PDW states.Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing ($p_x,p_y$) or ($d_{xz}, d_{yz})$ orbitals on the square lattice. For minimal interorbital $t$-$J$ or $t$-$V$ on-site interactions, a random phase approximation uncovers regimes of instability towards incommensurate $d_{xy}$ pair density wave ($d$-PDW) superconductivity with driven by interband pairing. We study the competition of PDW order with uniform nodal $d_{xy}$ pairing states and magnetic and charge density wave (CDW) instabilities. At strong coupling, we derive an effective hard-core Cooper pair Hamiltonian which we study using a bosonic Gutzwiller ansatz to reveal a period-$2$ PDW over a wide range of fillings as well as a checkerboard CDW at quarter-filling. Our results apply to correlated multi-orbital materials with quasi-1D bands, Hubbard models on the square-octagon lattice, and atomic fermions in $p$-orbitals. Our work highlights the role of the orbital content and multiband Fermi surfaces in stabilizing interband PDW states.

arXiv:2604.07511Apr 8, 20260 citations

Detection of pairing correlation in the two-dimensional Hubbard model

Kazuhiko Kuroki, Hideo Aoki, Takashi Hotta +1 more

The quantum Monte Carlo method is used to reexamine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a ``correlated pairing,'' 〈c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\uparrow}}}$c-${\mathrm{tilde}}_{{\mathrm{i}}^{|\mathrm{I}\mathrm{H}}\mathrm{\ensuremath{\downarrow}}}$〉 with c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\equiv}${\mathrm{c}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$(1-${\mathrm{n}}_{\mathrm{i}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$), which is inferred from the t-J model, the strong-coupling limit of the Hubbard model. The pairing in the d-wave channel is found to possess both a divergence like 1/T in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.The quantum Monte Carlo method is used to reexamine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a ``correlated pairing,'' 〈c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\uparrow}}}$c-${\mathrm{tilde}}_{{\mathrm{i}}^{|\mathrm{I}\mathrm{H}}\mathrm{\ensuremath{\downarrow}}}$〉 with c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\equiv}${\mathrm{c}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$(1-${\mathrm{n}}_{\mathrm{i}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$), which is inferred from the t-J model, the strong-coupling limit of the Hubbard model. The pairing in the d-wave channel is found to possess both a divergence like 1/T in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.

arXiv:cond-mat/9606143Physical review. B, Condensed matterFeb 1, 199710 citations

Phase diagram of the extended Hubbard model with pair hopping interaction

G. I. Japaridze, Sarkar, S.

A one-dimensional model of interacting electrons with on-site U, nearest- neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, \U - 2V\ < \2W\ and a bond-spin-density-wave (BSDW) for W > 0, \U - 2V\ < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the eta(pi) -superconducting phase at \U - 2V\ much less than 2t less than or equal to W is briefly discussed.A one-dimensional model of interacting electrons with on-site U, nearest- neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, \U - 2V\ < \2W\ and a bond-spin-density-wave (BSDW) for W > 0, \U - 2V\ < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the eta(pi) -superconducting phase at \U - 2V\ much less than 2t less than or equal to W is briefly discussed.

Jan 1, 200217 citations

Antiferromagnetism, Superconductivity and Phase Diagram in the Two-Dimensional Hubbard Model —Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model III—

Takashi Yanagisawa

We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$ , where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion $U$ , the band parameter $t'$ and the electron density $n_e$ . We show a phase diagram that includes superconducting and antiferromagnetic phases and that $t'=0$ is most favorable for superconductivity.We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$, where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion $U$, the band parameter $t'$ and the electron density $n_e$. We show a phase diagram that includes superconducting and antiferromagnetic phases and that $t'=0$ is most favorable for superconductivity.

arXiv:1903.09368Journal of the Physical Society of JapanApr 5, 201913 citations

{\mathit{U}}_{\mathit{c}}

(n), although no explicit attraction between particles is present in the Hamiltonian. The presence of a bound state for two particles in vacuum in D=1 and 2 (but not for D=3) suggests that, at low density and low dimensionality, superconductivity is due to condensation of preexistent pairs (dimers). The one-dimensional (1D) phase diagram is studied analytically as well as numerically and shows a transiiton between a Luttinger liquid and a strong-coupling phase with diverging superconducting susceptibility. Estimates of critical exponents are given at low density and at quarter filling for several values of the parameters. The 2D model at quarter filling is analyzed by Lanczos diagonalization on a 4\ifmmode\times\else\texttimes\fi{}4 cluster. The numerical results are consistent with the phase diagram obtained by BCS mean-field theory and is qualitatively similar to the 1D case: a ground state with spin gap and off-diagonal long-range order at U

{\mathit{U}}_{\mathit{c}}

(n); and a Fermi liquid above

{\mathit{U}}_{\mathit{c}}

with no sign of phase separation.

Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing (

p_x,p_y

) or (

d_{xz}, d_{yz})

orbitals on the square lattice. For minimal interorbital

t

J

t

V

on-site interactions, a random phase approximation uncovers regimes of instability towards incommensurate

d_{xy}

pair density wave (

d

-PDW) superconductivity with driven by interband pairing. We study the competition of PDW order with uniform nodal

d_{xy}

pairing states and magnetic and charge density wave (CDW) instabilities. At strong coupling, we derive an effective hard-core Cooper pair Hamiltonian which we study using a bosonic Gutzwiller ansatz to reveal a period-

2

PDW over a wide range of fillings as well as a checkerboard CDW at quarter-filling. Our results apply to correlated multi-orbital materials with quasi-1D bands, Hubbard models on the square-octagon lattice, and atomic fermions in

p

-orbitals. Our work highlights the role of the orbital content and multiband Fermi surfaces in stabilizing interband PDW states.

ψ=\exp(-λK)P_Gψ_0

, where

ψ_0

is a one-particle state,

P_G

is the Gutzwiller operator,

K

is the kinetic operator, and

λ

is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion

U

, the band parameter

t'

and the electron density

n_e

. We show a phase diagram that includes superconducting and antiferromagnetic phases and that

t'=0

is most favorable for superconductivity.