On-site attractive multiorbital Hamiltonian for d-wave superconductors

Christopher B. Bishop; Guangkun Liu; Elbio Dagotto; Adriana Moreo

doi:10.1103/PhysRevB.93.224519

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On-site attractive multiorbital Hamiltonian for d-wave superconductors

Christopher B. Bishop, Guangkun Liu, Elbio Dagotto, Adriana Moreo

DOI 10.1103/PhysRevB.93.224519 · Physical Review B

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Abstract

We introduce a two-orbital Hamiltonian on a square lattice that contains on-site attractive interactions involving the two eg orbitals. Via a canonical mean-field procedure similar to the one applied to the well-known negative-U Hubbard model, it is shown that the model develops d-wave (B1g) superconductivity with nodes along the diagonal directions of the square Brillouin zone. This result is also supported by exact diagonalization of the model in a small cluster. The expectation is that this relatively simple attractive model could be used to address the properties of multiorbital d-wave superconductors in the same manner that the negative-U Hubbard model is widely applied to the study of the properties of s-wave single-orbital superconductors. In particular, we show that by splitting the eg orbitals and working at three-quarters filling, such that the x2−y2 orbital dominates at the Fermi level but the 3z2−r2 orbital contribution is nonzero, the d-wave pairing state found here phenomenologically reproduces several properties of the superconducting state of the high Tc cuprates.