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

Pairing instabilities in the two-dimensional Hubbard model

Andrey V. Chubukov, Jianping Lü

Published May 12, 2023• 0 citations
Publisher

Abstract

We show that for low and moderate fillings the ground state of the two-dimensional Hubbard model with positive-U and nearest-neighbor hopping is unstable with respect to d-wave pairing with dxy symmetry of the gap wave function: Δ∼sinkxsinky. The inclusion of the next-neighbor hopping may either suppress the pairing or change the symmetry of the superconducting state.

DOI
10.17615/dm6w-kr13

Related papers

Pairing instabilities in the two-dimensional Hubbard model

Andrey V. Chubukov, Jian Ping Lu

We show that for low and moderate fillings the ground state of the two-dimensional Hubbard model with positive-U and nearest-neighbor hopping is unstable with respect to d-wave pairing with ${\mathit{d}}_{\mathit{x}\mathit{y}}$ symmetry of the gap wave function: \ensuremath{\Delta}\ensuremath{\sim}sin${\mathit{k}}_{\mathit{x}}$sin${\mathit{k}}_{\mathit{y}}$. The inclusion of the next-neighbor hopping may either suppress the pairing or change the symmetry of the superconducting state.

Physical review. B, Condensed matter•Nov 1, 1992•38 citations

Superconductivity in the two-dimensional t - t′ -Hubbard model

Andreas Eberlein, Walter Metzner

Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for $d$-wave superconductivity in the ground state of the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable ${t}^{\ensuremath{'}}$ is necessary to obtain a sizable pairing gap.

arXiv:1308.4845•Physical Review B•Jan 17, 2014•72 citations

Superconductivity in a strongly correlated electron system: A theoretical study

E.S. Caixeiro, A. Troper

In this work we study the superconductivity within an attractive two-dimensional one-band Hubbard model. We consider a d-wave superconducting gap and a Hubbard-I approximation to describe the strongly correlated superconducting regime. We use the Green’s function method to obtain the order parameter Δ and the superconducting critical temperature Tc. The results show that for fixed values of the superconducting attractive potential U(U<0), the gap increases for low temperatures but diminishes abruptly as the temperature increases. The effect of pressure is discussed, varying the next-nearest-neighbor hopping t2, yielding a change in Tc, and also in Δ0, and a tendency to suppress the superconductivity.

Journal of Applied Physics•Feb 17, 2009•3 citations

Enhanced pairing in the repulsive Hubbard model with next-nearest-neighbor hopping

Raimundo R. dos Santos

We study the behavior of pair susceptibilities in the two-dimensional repulsive Hubbard model with next-nearest-neighbor hopping ${t}_{2}$ by Monte Carlo simulations. In a certain range of band filling, we find that the d-wave pair susceptibilities can be enhanced by a Hubbard repulsion U with respect to the noninteracting case, unlike the case with ${t}_{2}$=0. We discuss the connection of this model to ${\mathrm{CuO}}_{2}$ planes in the oxide superconductors and the possible implication of our results for these materials.

Physical review. B, Condensed matter•Apr 1, 1989•28 citations

Superconducting Phase and Pairing Fluctuations in the Half-Filled Two-Dimensional Hubbard Model

Michael A. Sentef, Philipp Werner, Emanuel Gull +1 more

The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.

arXiv:1102.1911•Physical Review Letters•Sep 14, 2011•40 citations

Electron doping and superconductivity in the two-dimensional Hubbard model

David Eichenberger, D. Baeriswyl

An elaborate variational wave function is used for studying superconductivity in the (repulsive) two-dimensional Hubbard model, including both nearest- and next-nearest-neighbor hoppings. A marked asymmetry is found between the ``localized'' hole-doped region and the more itinerant electron-doped region. Superconductivity with $d$-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.

Physical Review B•Mar 31, 2009•12 citations
We show that for low and moderate fillings the ground state of the two-dimensional Hubbard model with positive-U and nearest-neighbor hopping is unstable with respect to d-wave pairing with dxy symmetry of the gap wave function: Δ∼sinkxsinky. The inclusion of the next-neighbor hopping may either suppress the pairing or change the symmetry of the superconducting state.
We show that for low and moderate fillings the ground state of the two-dimensional Hubbard model with positive-U and nearest-neighbor hopping is unstable with respect to d-wave pairing with dxy{\mathit{d}}_{\mathit{x}\mathit{y}}dxy​ symmetry of the gap wave function: \ensuremath{\Delta}\ensuremath{\sim}sinkx{\mathit{k}}_{\mathit{x}}kx​sinky{\mathit{k}}_{\mathit{y}}ky​. The inclusion of the next-neighbor hopping may either suppress the pairing or change the symmetry of the superconducting state.
Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for ddd-wave superconductivity in the ground state of the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable ${t}^{\ensuremath{'}}$ is necessary to obtain a sizable pairing gap.
In this work we study the superconductivity within an attractive two-dimensional one-band Hubbard model. We consider a d-wave superconducting gap and a Hubbard-I approximation to describe the strongly correlated superconducting regime. We use the Green’s function method to obtain the order parameter Δ and the superconducting critical temperature Tc. The results show that for fixed values of the superconducting attractive potential U(U<0), the gap increases for low temperatures but diminishes abruptly as the temperature increases. The effect of pressure is discussed, varying the next-nearest-neighbor hopping t2, yielding a change in Tc, and also in Δ0, and a tendency to suppress the superconductivity.
We study the behavior of pair susceptibilities in the two-dimensional repulsive Hubbard model with next-nearest-neighbor hopping t2{t}_{2}t2​ by Monte Carlo simulations. In a certain range of band filling, we find that the d-wave pair susceptibilities can be enhanced by a Hubbard repulsion U with respect to the noninteracting case, unlike the case with t2{t}_{2}t2​=0. We discuss the connection of this model to CuO2{\mathrm{CuO}}_{2}CuO2​ planes in the oxide superconductors and the possible implication of our results for these materials.
The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.
An elaborate variational wave function is used for studying superconductivity in the (repulsive) two-dimensional Hubbard model, including both nearest- and next-nearest-neighbor hoppings. A marked asymmetry is found between the ``localized'' hole-doped region and the more itinerant electron-doped region. Superconductivity with ddd-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.