On-site Atractive Multiorbital Hamiltonian for $d$-Wave Superconductors

Abstract

We introduce a two-orbital Hamiltonian on a square lattice that contains on-site attractive interactions involving the two $e_g$ 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 new model develops $d$-wave ($B_{1g}$) 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 $e_g$ orbitals and working at three-quarters filling, such that the $x^2-y^2$ orbital dominates at the Fermi level but the $3z^2-r^2$ orbital contribution is nonzero, the $d$-wave pairing state found here phenomenologically reproduces several properties of the superconducting state of the high $T_c$ cuprates.

References in corpus (8)

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Cited by in corpus (8)

• Classification of multipole superconductivity in multi-orbital systems and its implications
• Direct Observation of Orbital Hybridisation in a Cuprate Superconductor
• Two-dimensional type-II Dirac fermions in layered oxides
• Minimal-size Real Space d-wave Pairing Operator in CuO2 Planes
• Local nodal Cooper pairs in multiorbital systems
• Charge Oscillations Emerging after Application of an Intense Light Field to Superconductors on a Dimer Lattice
• Octupolar edge state in an $e_g$ orbital system on a square lattice
• Flat Surface State with Octupole Moment in an $e_g$ Orbital System on a Simple Cubic Lattice