Superconductivity in the two-dimensional Hubbard model

Abstract

Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (π, 0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. Singlet d x 2 −y 2 -wave pairing is strongly favoured and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest neighbour antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favouring superconductivity. However the mechanism for superconductivity is a local one, in contrast to spin fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature T c is in the range 10-100K. The optimum doping δ c lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2∆

Role of hybridization in the superconducting properties of an extended d–p Hubbard model: a detailed numerical study

“…While the role of the k-independent term is only to shift the poles of the Green's function, the k-dependent part causes a flattening at the top of the lower band from around k = (π, π) until k = (π, 0) as can be verified in Refs. [6,8]. This flattening occurs because W d kσ decreases when ε d k increases, as discussed in Ref.…”

“…[3], considering the particular case with singlet pairing and the d-wave symmetry, we get d i−σ d iσ = 0 and l d i−σ d lσ = 0, where the sum is over sites l which are nearest neighbors of i. Therefore, in the d-wave case [6], the superconducting gap is determined by the gap function,…”

“…In the previous work [3], we improved Ref. [5] to also include superconducting properties following closely the approach introduced by Beenen and Edwards [6]. Nevertheless, in Ref.…”

“…The gap function given by equation (2), defined in Ref. [6], is solved self-consistently. The band shift W kσ = W d kσ + W pd σ , shifts the poles of the propagators G 1s kσ .…”

Hubbard-I approximation as a tool for study of superconducting properties of the Hubbard model with repulsive interaction

“…Substituting (19) in (18), we obtain the equation of motion for the propagator P ijlm in the Hubbard-I approximation valid when i = j and l = m ∂ ∂τ + 2µ…”