Hole Dispersion and Symmetry of the Superconducting Order Parameter for Underdoped CuO${}_2$ Bilayers and 3D Antiferromagnets

Abstract

We calculate the dispersion of a hole in $\mathrm{Cu}{\mathrm{O}}_2$ bilayers and 3D antiferromagnets, using the self-consistent Born approximation (SCBA) to the $t-J$ model. Superconductivity and the symmetry of its order parameter are studied introducing a nearest-neighbor density-density attraction induced by short range antiferromagnetic (AF) fluctuations, as described in recent studies for the single layer cuprates. The well-known pairing in the $d_{x^2-y^2}$ channel observed for one plane remains robust when three dimensional interactions are turned on. In bilayers, as the exchange along the direction perpendicular to the planes grows, eventually a transition to a ``s-wave'' state is observed with an order parameter mixture of $d_{3z^2-r^2}$ and $s_{x^2+y^2+z^2}$. For an isotropic 3D antiferromagnet the $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ channels are degenerate.

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• Spectral and Transport Properties of Quantum Wires with Bond Disorder
• ARPES Spectral Function in Lightly Doped and Antiferromagnetically Ordered YBa2Cu3O{6+y}
• Equilibrium and non-equilibrium dynamics of a hole in a bilayer antiferromagnet
• Dynamics of a single hole in the Heisenberg-Kitaev model: a self-consistent Born approximation study