The Hubbard model and its extensions are important microscopic models for understanding high- ${T}_{c}$ superconductivity in cuprates. In the model with next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ (the ${t}^{\ensuremath{'}}$-Hubbard model), pairing is strongly influenced by ${t}^{\ensuremath{'}}$. In particular, a recent study on a width-4 cylinder observed quasi-long-range superconducting order, associated with a negative ${t}^{\ensuremath{'}}$, which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-$4\phantom{\rule{4pt}{0ex}}{t}^{\ensuremath{'}}$-Hubbard model. We show that in this specific system, the pairing symmetry with ${t}^{\ensuremath{'}}<0$ 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 ${t}^{\ensuremath{'}}$ suppresses the conventional $d$ -wave, leading to plaquette pairing. In contrast, a different ${t}^{\ensuremath{'}\ensuremath{'}}$ coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional $d$ -wave pairing.The Hubbard model and its extensions are important microscopic models for understanding high-${T}_{c}$ superconductivity in cuprates. In the model with next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ (the ${t}^{\ensuremath{'}}$-Hubbard model), pairing is strongly influenced by ${t}^{\ensuremath{'}}$. In particular, a recent study on a width-4 cylinder observed quasi-long-range superconducting order, associated with a negative ${t}^{\ensuremath{'}}$, which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-$4\phantom{\rule{4pt}{0ex}}{t}^{\ensuremath{'}}$-Hubbard model. We show that in this specific system, the pairing symmetry with ${t}^{\ensuremath{'}}<0$ 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 ${t}^{\ensuremath{'}}$ suppresses the conventional $d$-wave, leading to plaquette pairing. In contrast, a different ${t}^{\ensuremath{'}\ensuremath{'}}$ coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional $d$-wave pairing.

arXiv:2004.03001Physical review. B./Physical review. BJul 6, 202086 citations

D-wave pairing in the two-dimensional Hubbard model with low filling

M. A. Baranov, M. Yu. Kagan

The European Physical Journal BJun 1, 199246 citations

Triplet p-wave superconductivity in the low-density extended hubbard model with Coulomb repulsion

M. Yu. Kagan, Dmitri V. Efremov, M. S. Mar’enko +1 more

We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density (n el → 0) on simple cubic (square) lattice. We show that in a realistic strong-coupling case U ≫ V ≫ W (U and V are the onsite and the intersite Coulomb repulsions, respectively, and W the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V = 0.We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density (n el → 0) on simple cubic (square) lattice. We show that in a realistic strong-coupling case U ≫ V ≫ W (U and V are the onsite and the intersite Coulomb repulsions, respectively, and W the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V = 0.

arXiv:1105.4704Journal of Experimental and Theoretical Physics LettersAug 1, 201131 citations

On d-wave pairing in one band Hubbard model

Nikolay M. Plakida, V. Yu. Yushankhaï, Ihor V. Stasyuk

Physica C SuperconductivityDec 1, 198928 citations

The Hubbard model and its extensions are important microscopic models for understanding high-

{T}_{c}

superconductivity in cuprates. In the model with next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ (the ${t}^{\ensuremath{'}}$-Hubbard model), pairing is strongly influenced by ${t}^{\ensuremath{'}}$. In particular, a recent study on a width-4 cylinder observed quasi-long-range superconducting order, associated with a negative ${t}^{\ensuremath{'}}$, which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-$4\phantom{\rule{4pt}{0ex}}{t}^{\ensuremath{'}}$-Hubbard model. We show that in this specific system, the pairing symmetry with ${t}^{\ensuremath{'}}<0$ 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 ${t}^{\ensuremath{'}}$ suppresses the conventional

d

-wave, leading to plaquette pairing. In contrast, a different ${t}^{\ensuremath{'}\ensuremath{'}}$ coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional

d

-wave pairing.