Superconducting instabilities of the non-half-filled Hubbard model in two dimensions

Abstract

The problem of weakly correlated electrons on a square lattice is formulated in terms of one-loop renormalization group. Starting from the action for the entire Brillouin zone (and not with a low-energy effective action) we reduce successively the cutoff Λ about the Fermi surface and follow the renormalization of the coupling U as a function of three energy-momenta. We calculate the intrinsic scale T co where the renormalization group flow crosses over from the regime (Λ > T co ) where the electron-electron (e-e) and electron-hole (eh) terms are equally important to the regime (Λ < T co ) where only the e-e term plays a role. In the low energy regime only the pairing interaction V is marginally relevant, containing contributions from all renormalization group steps of the regime Λ > T co . After diagonalization of V Λ=Tco , we identify its most attractive eigenvalue λ min . At low filling, λ min corresponds to the B 2 representation (d xy symmetry), while near half filling the strongest attraction occurs in the B 1 representation (d x 2 −y 2 symmetry). In the direction of the van Hove singularities, the order parameter shows peaks with increasing strength as one approaches half filling. Using the form of pairing and the structure of the renormalization group equations in the low energy regime, we give our interpretation of ARPES experiments trying to determine the symmetry of the order parameter in the Bi2212 high-T c compound.

Order-parameter symmetries for magnetic and superconducting instabilities: Bethe-Salpeter analysis of functional renormalization-group solutions

“…[13][14][15]. Recently, the interplay of antiferromagnetism and d-wave superconductivity (dSC) and ferromagnetism and p-wave superconductivity (pSC), respectively, was reconsidered within the tt ′ Hubbard model using functional renormalization-group (fRG) techniques [16][17][18][19][20]. Early versions of fRG [16][17][18], which used the momentum cutoff procedure, were unable to search for ferromagnetism.…”

“…This drawback is overcome in the temperature-cutoff fRG approach (TCRG) [19], which proved successful in describing both, AFM and FM instabilities together with singlet-and triplet superconducting pairing in the weak-coupling t-t ′ Hubbard model and its extensions in a broad parameter range [19][20][21]. In the previous fRG analyses it has been a common practice to assume order parameter structures, which have the form of square lattice basis functions with s-, p-or d-wave symmetry [16][17][18][19][20][21]. Although it was recognized that in the RG flow of the order parameter susceptibilities also the momentum dependence acquires specific corrections to their initial form [17,[19][20][21][22], these corrections were so far not analyzed in detail.…”

“…Recently, the interplay of antiferromagnetism and d-wave superconductivity (dSC) and ferromagnetism and p-wave superconductivity (pSC), respectively, was reconsidered within the tt ′ Hubbard model using functional renormalization-group (fRG) techniques [16][17][18][19][20]. Early versions of fRG [16][17][18], which used the momentum cutoff procedure, were unable to search for ferromagnetism. This drawback is overcome in the temperature-cutoff fRG approach (TCRG) [19], which proved successful in describing both, AFM and FM instabilities together with singlet-and triplet superconducting pairing in the weak-coupling t-t ′ Hubbard model and its extensions in a broad parameter range [19][20][21].…”

W= 0 pairing in Hubbard and related models of low-dimensional superconductors

“…We want to study the doped antiferromagnet since there are strong indications that the Fermi liquid is unstable towards pairing near half filling; they come from diagrammatic approaches [15], renormalization group techniques [16], [17] and also cluster diagonalizations [32]. Therefore exact results on the half filled Hubbard Model may be relevant to antiferromagnetism and to the mechanism of the superconducting instability as well.…”

“…Renormalization Group (RG) methods [13] are a well controlled alternative approach to deal with Fermi systems having competing singularities. The RG has been used by several authors [16], [17], [18] to study the coupling flows at different particle densities. In agreement with the previous findings, RG calculations show a d-wave superconducting instability away from half filling.…”