Magnetism and d-wave superconductivity on the half-filled square lattice with frustration

Abstract

The role of frustration and interaction strength on the half-filled Hubbard model is studied on the square lattice with nearest and next-nearest neighbour hoppings t and t' using the Variational Cluster Approximation (VCA). At half-filling, we find two phases with long-range antiferromagnetic (AF) order: the usual Neel phase, stable at small frustration t'/t, and the so-called collinear (or super-antiferromagnet) phase with ordering wave-vector $(\pi ,0)$ or $(0,\pi )$, stable for large frustration. These are separated by a phase with no detectable long-range magnetic order. We also find the d-wave superconducting (SC) phase ($d_{x^2-y^2}$), which is favoured by frustration if it is not too large. Intriguingly, there is a broad region of coexistence where both AF and SC order parameters have non-zero values. In addition, the physics of the metal-insulator transition in the normal state is analyzed. The results obtained with the help of the VCA method are compared with the large-U expansion of the Hubbard model and known results for the frustrated J1-J2 Heisenberg model. These results are relevant for pressure studies of undoped parents of the high-temperature superconductors: we predict that an insulator to d-wave SC transition may appear under pressure.

12 pages, 10 figures

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• Low energy theory of the t-t'-t''-U Hubbard Model at half-filling: interaction strengths in cuprate superconductors and an effective spin-only description of La_2CuO_4
• Mott transition and magnetism of the triangular-lattice Hubbard model with next-nearest-neighbor hopping
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• Magnetoresistance scaling in the layered cobaltate Ca3Co4O9
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• Orbital Nematic Order and Interplay with Magnetism in the Two-Orbital Hubbard Model
• Mott transition and magnetism on the anisotropic triangular lattice
• Optimal inhomogeneity for pairing in Hubbard systems with next-nearest-neighbor hopping
• Magnetic phase diagram and Mott transition of the half-filled 1/5-depleted Hubbard model with frustration
• Zero-temperature Phase Diagram of Two Dimensional Hubbard Model