Superconductivity in an extended Hubbard model with attractive interaction

Abstract

In this work, a two-dimensional one-band Hubbard model is investigated within a two-pole approximation. The model presents a non-local attractive potential U (U < 0) that allows the study of d-wave superconductivity and also includes hopping up to second-nearest-neighbors. The twopole scheme has been proposed to improve the Hubbard-I approximation. The analytical results show a more complex form for the gap ∆(T ), when compared to the one obtained in the latter approximation. Indeed, new anomalous correlation functions associated with the superconductivity are involved in the calculation of ∆(T ). Numerical results in a range of temperatures are presented.Moreover, the structure of the quasiparticle bands and the topology of the Fermi surface are studied in detail in the normal state. Connections with some experimental results are also included.

Specific heat of a non-local attractive Hubbard model

“…The right panel in figure 1 shows that | S i · S j | is large at low temperatures and increases with |G|. As discussed in references [5,6,15], the S i · S j modify the renormalized band structure by enlarging the flat region near the anti-nodal points (π, 0) and (0, π). As a consequence, a pronounced peak emerges on the density of state.…”

“…The mechanism discussed in the previous paragraph also favors the existence of d-wave superconductivity in the attractive non-local Hubbard model [5]. This occurs because the magnetic correlations enhance the density of states at the van Hove singularity (VHS) providing more electrons able to form superconducting pairs.…”

“…The model investigated is a two-dimensional one-band Hubbard model [5,10] which is given by: where d † iσ (d iσ ) is the fermionic creation (annihilation) operator at site i with spin σ = {↑, ↓} and n i,σ = d † iσ d iσ is the number operator. The quantity t i j represents the hopping between sites i and j and ... indicates the sum over the first and the second-nearest-neighbors of i and µ is the chemical potential.…”

“…Quite recently, an attractive Hubbard model with non-local interaction [5,6] has been considered using a two pole approximation [7,8]. Although our model is not fully realistic for HTSC, it allows superconductivity with d x 2 −y 2 −wave symmetry [9] and also can be quite useful to bring information on the possible sources of the pseudogap.…”

“…In Refs. [5,6], it has been obtained the evolution of the Fermi surface from a closed shape to a hole pocket shape as well as the behavior of the χ with a maximum at δ * where δ = 1 − n T (n T = n ↑ + n ↓ ), and then, decreasing when δ < δ * . Remarkably, both results can be traced from one single mechanism, i. e., from short range antiferromagnetic (AF) correlations.…”