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

• Published in: Physical review. B 2020-07, Vol.102 (4), p.1, Article 041106
• Main Authors: Chung, Chia-Min, Qin, Mingpu, Zhang, Shiwei, Schollwöck, Ulrich, White, Steven R.
• Format: Article
• Language: English
• Subjects: Cuprates; Cylinders; Superconductivity
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.102.041106

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.