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arXiv:2209.05192 · Physical review. B./Physical review. B

Pair binding and enhancement of pairing correlations in asymmetric Hubbard ladders

Anas Abdelwahab, Gökmen Polat, Eric Jeckelmann

Published Mar 7, 2023• 3 citations
arXivHTMLPDF

Abstract

Asymmetric two-leg Hubbard ladders with different on-site interactions ${U}_{y}$ and hoppings ${t}_{y}$ on each leg are investigated using the density-matrix renormalization group method and exact diagonalizations. The pairing found in symmetric ladders is robust against the introduction of the leg asymmetry. When studying pairing, one-band Hubbard ladder models are better described as one-dimensional correlated two-band models than as sublattices of higher-dimensional systems. The asymmetric Hubbard ladder provides us with a simple model for studying pairing in the crossover regime between charge-transfer and Mott insulators.

DOI
10.1103/physrevb.107.125117

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Asymmetric two-leg Hubbard ladders with different on-site interactions Uy{U}_{y}Uy​ and hoppings ty{t}_{y}ty​ on each leg are investigated using the density-matrix renormalization group method and exact diagonalizations. The pairing found in symmetric ladders is robust against the introduction of the leg asymmetry. When studying pairing, one-band Hubbard ladder models are better described as one-dimensional correlated two-band models than as sublattices of higher-dimensional systems. The asymmetric Hubbard ladder provides us with a simple model for studying pairing in the crossover regime between charge-transfer and Mott insulators.
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We study signatures of superconductivity in a two-leg ``checkerboard'' Hubbard ladder model, defined as a one-dimensional (period 2) array of square plaquettes with an intraplaquette hopping ttt and interplaquette hopping ${t}^{\ensuremath{'}}$, using the density-matrix renormalization-group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half-filling, $U\ensuremath{\approx}6t$ and ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.6$. Other forms of modulated hopping parameters, with periods of either one or three lattice constants, are also found to enhance pairing relative to the uniform two-leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.
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Previous studies have shown that bipartite Hubbard systems with inhomogeneous hopping amplitudes can exhibit higher pair-binding energies than the uniform model. Here we examine whether this result holds for systems with a more generic band structure. To this end, we use exact diagonalization and the density matrix renormalization-group method to study the $4\ifmmode\times\else\texttimes\fi{}4$ Hubbard cluster and the two-leg Hubbard ladder with checkerboard-modulated nearest-neighbor hopping, ttt, and next-nearest-neighbor (diagonal) hopping, td{t}_{d}td​. We find that the strongest pairing continues to occur at an intermediate level of inhomogeneity. While the maximal pair-binding energy is enhanced by a positive td/t{t}_{d}/ttd​/t, it is suppressed and appears at weaker repulsion strengths and lower hole concentrations when td/t{t}_{d}/ttd​/t is negative. We point out a possible connection between the pairing maximum and the magnetic properties of the system.
Here we report results of a density-matrix-renormalization-group calculation of the charge, spin, and pairing properties of a two-leg CuO Hubbard ladder. The outer oxygen atoms as well as the rung and leg oxygen atoms are included along with near-neighbor and oxygen-hopping matrix elements. This model allows us to study the effects of hole and electron doping on a system that is a charge-transfer insulator at a filling of one hole per Cu and exhibits power law, d-wave-like pairing correlations when doped. In particular, we focus on the differences between doping with holes and with electrons.
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