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arXiv:1602.02420 · Physical review. B./Physical review. B

On-site attractive multiorbital Hamiltonian for d -wave superconductors

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

Published Jun 29, 2016• 10 citations
arXivHTMLPDF

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 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 ${x}^{2}\ensuremath{-}{y}^{2}$ orbital dominates at the Fermi level but the $3{z}^{2}\ensuremath{-}{r}^{2}$ 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.

DOI
10.1103/physrevb.93.224519

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We introduce a two-orbital Hamiltonian on a square lattice that contains on-site attractive interactions involving the two eg{e}_{g}eg​ orbitals. Via a canonical mean-field procedure similar to the one applied to the well-known negative-UUU Hubbard model, it is shown that the model develops ddd-wave (B1g{B}_{1g}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 ddd-wave superconductors in the same manner that the negative-UUU Hubbard model is widely applied to the study of the properties of sss-wave single-orbital superconductors. In particular, we show that by splitting the eg{e}_{g}eg​ orbitals and working at three-quarters filling, such that the x2\ensuremath−y2{x}^{2}\ensuremath{-}{y}^{2}x2\ensuremath−y2 orbital dominates at the Fermi level but the 3z2\ensuremath−r23{z}^{2}\ensuremath{-}{r}^{2}3z2\ensuremath−r2 orbital contribution is nonzero, the ddd-wave pairing state found here phenomenologically reproduces several properties of the superconducting state of the high Tc{T}_{c}Tc​ cuprates.
Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing (px,pyp_x,p_ypx​,py​) or (dxz,dyz)d_{xz}, d_{yz})dxz​,dyz​) orbitals on the square lattice. For minimal interorbital ttt-JJJ or ttt-VVV on-site interactions, a random phase approximation uncovers regimes of instability towards incommensurate dxyd_{xy}dxy​ pair density wave (ddd-PDW) superconductivity with driven by interband pairing. We study the competition of PDW order with uniform nodal dxyd_{xy}dxy​ pairing states and magnetic and charge density wave (CDW) instabilities. At strong coupling, we derive an effective hard-core Cooper pair Hamiltonian which we study using a bosonic Gutzwiller ansatz to reveal a period-222 PDW over a wide range of fillings as well as a checkerboard CDW at quarter-filling. Our results apply to correlated multi-orbital materials with quasi-1D bands, Hubbard models on the square-octagon lattice, and atomic fermions in ppp-orbitals. Our work highlights the role of the orbital content and multiband Fermi surfaces in stabilizing interband PDW states.
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The authors study a simple model for superconductivity based on an extended Hubbard model with on-site repulsive and inter-site attractive interaction for arbitrary electron density. The two-dimensional square lattice d-wave pairing is most stable for a nearly half-filled band. p-wave and then extended s-wave pairing become stable upon decreasing band filling. Competition between the various anisotropic pairings and antiferromagnetism as well as the effect of next-nearest-neighbour hopping is discussed. The authors relate the present model to high-T c superconducting oxides.
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