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Physical review. B, Condensed matter

Pairing instabilities in the two-dimensional Hubbard model

Andrey V. Chubukov, Jian Ping Lu

Published Nov 1, 1992• 38 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 ${\mathit{d}}_{\mathit{x}\mathit{y}}$ 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.

DOI
10.1103/physrevb.46.11163

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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.
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.
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.
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.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (JJJ) and correlated hopping (KKK) interaction. Detailed numerical analysis of sss-, ppp-, and ddd-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (ttt) and next-nearest- (t2{t}_{2}t2​) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the ddd-wave and the extended sss-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the t2t\frac{{t}_{2}}{t}tt2​​ ratio, giving in particular for t2=0{t}_{2}=0t2​=0 sss-wave (ddd-wave) pairing as most favorable in the low (high) density limit, but increasing t2{t}_{2}t2​ can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects sss-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.