Plaquette versus ordinary d-wave pairing in the t′-Hubbard model on a width-4 cylinder

The Hubbard model and its extensions are important microscopic models for understanding high-Tc superconductivity in cuprates. In the model with next-nearest-neighbor hopping t' (the t'-Hubbard model), pairing is strongly influenced by t'. In particular, a recent study on a width-4 cylinder observed quasi-long-range superconducting order, associated with a negative t', which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-4 t'-Hubbard model. We show that in this specific system, the pairing symmetry with t' < 0 is not the ordinary d-wave one would expect in the 2D limit. Instead we observe a so-called plaquette d-wave pairing. We show that the plaquette d-wave or its extension is difficult to generalize in other geometries, for example a 4-leg ladder with open boundaries or a width-6 cylinder. We find that a negative t' suppresses the conventional d-wave, leading to plaquette pairing. In contrast, a different t '' coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional d-wave pairing.