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Physica C Superconductivity

Superconducting correlations in the two-dimensional Hubbard model with long-range electron hopping

Pavol Farkašovský

Published Sep 5, 2022• 4 citations
Publisher
DOI
10.1016/j.physc.2022.1354141

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The Hubbard and related models serve as a fundamental starting point in understanding the novel experimental phenomena in correlated electron materials, such as superconductivity, Mott insulator, magnetism. Recent numerical simulations demonstrate that the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a key role for the superconductivity. However, the impacts of long-range intersite interactions in such a ${t}^{\ensuremath{'}}$-Hubbard model are less explored. Using the state-of-art density-matrix renormalization group method, we investigate the ${t}^{\ensuremath{'}}$-Hubbard model on a two-leg ladder with the intersite interactions extended to the fourth neighbors. The numerical results show that the quasi-long-range superconducting correlation remains stable under the repulsive intersite interactions and these long-range repulsive interactions only change the ground state quantitatively. In addition, inspired by recent experiments on one-dimensional cuprate chain ${\mathrm{Ba}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$, we find that the nearest-neighbor attractive interaction significantly enhances the superconducting correlation when it is comparable to the nearest-neighbor hopping ttt. Stronger attraction drives the system into an electron-hole phase separation. Finally, we discuss the effects of the on-site interaction on superconductivity.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine ferromagnetism in the one-dimensional Hubbard model with long-range and correlated hopping. It is found that the correlated hopping term stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n. The critical value of the interaction strength Uc above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model is presented for physically the most interesting cases. 1 The Hubbard model has become, since its inception [1] in 1963, one of the most popular examples of a system of interacting electrons with short-range interactions. It has been used in the literature to study a great variety of many-body effects in metals, of which ferromagnetism, metal-insulator transitions, charge-density waves and superconductivity are the most common examples. Of all these cooperative phenomena the problem of ferromagnetism in the Hubbard model has the longest
We present stochastic diagonalization results for the ground-state energy and the largest eigenvalue of the two-fermion density matrix of the BCS reduced Hamiltonian, the Hubbard model, and the Hubbard model with correlated hopping. The system-size dependence of this eigenvalue is used to study the existence of Off-Diagonal Long-Range Order in these models. We show that the model with correlated hopping and repulsive on-site interaction can exhibit Off-Diagonal Long-Range Order. Analytical results for some special limiting cases indicate that Off-Diagonal Long-Range Order not always implies superconductivity.