Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: a numerical RPA study

TL;DR

This study investigates the pairing symmetry in the 2D Hubbard model using a numerical RPA approach, revealing transitions between p-wave and d-wave symmetries influenced by Fermi surface topology and van Hove singularities.

Contribution

It provides a comprehensive phase diagram of pairing symmetries in the weak-coupling Hubbard model, highlighting the role of Fermi surface features and spin fluctuations in determining the superconducting gap structure.

Findings

Transition from p-wave to d-wave pairing as filling increases

Near van Hove singularity, triplet pairing becomes energetically favorable

Significant deviations from first harmonic gap structures in both singlet and triplet solutions

Abstract

We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from p-wave at very low electron fillings to d_{x^2-y^2}-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise sub-dominant triplet solution over the singlet d-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasi-particle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet d_{x^2-y^2} gap as well as the chiral triplet gap solution.