Intralayer-versus-interlayer pairing in the copper oxide superconductors

Abstract

We have investigated the competing roles of intralayer s-wave and interlayer BCS-like pairing in determining the c-axis versus ab-plane energy-gap anisotropy in layered superconductors with N=1,2 conducting planes per unit-cell edge s. For N=1, intralayer s-wave pairing leads to a conventional order parameter (OP) Δ0 with a transition temperature (Tc) value Tc0 and isotropic energy gap 2‖Δ0‖. For interlayer pairing, the four-vector gap function Δ̃3(kz) contains a singlet OP Δs and a vector triplet OP Δt, with corresponding normalized gap functions √2 coskzs and √2 sinkzs. Since Δs and Δt have identical Tc values (Tcs=Tct), the free energy is minimized when ‖Δs‖=‖Δt‖, and the resulting gap 2‖Δ‖ is found to be isotropic. However, 2‖Δ‖ is completely incompatible with 2‖Δ0‖. For N=2, there are two intralayer pairing OP’s Δ0 and Δ1, and two interlayer four-vector gap functions Δ̃3(kz) and Δ̃2(kz), all of which could contribute to measurable quantities in the Gaussian-fluctuation regime above the highest Tc value. However, interband pair breaking causes Δ1 and Δ̃2 to vanish below the maximum Tc value. Of the two singlet OP’s in Δ̃3(kz), the OP Δs has the higher Tc value, Tcs, and the second singlet OP can be neglected. The triplet OP Δt has the Tc value Tct≤Tcs. For Tc0>Tcs, the gap is just 2‖Δ0‖. For Tc0<Tct, Δ0=0 and the gap 2‖Δ(kz,T)‖ is anisotropic. There are two regions of the parameters with different gap-anisotropy behavior. In region I, the gap is always nodeless, and is nearly pure singlet for weak coupling. In region II, the gap has a pair of nodes near to Tcs, but is nodeless at low T, as ‖Δt‖≠0. For Tcs>Tc0>Tct, the gap 2‖Δ(kz,T)‖ is anisotropic, nodeless at low T, and could on rare occasions involve Δ0≠0, in addition to Δs≠0. In any event, the gap is the same on both of the quasiparticle bands. Our results are discussed in terms of recent far-infrared-reflectance, Raman-scattering, and point-contact-tunneling experiments. Additional experiments to clarify the c-axis versus ab-plane gap anisotropy and the microscopic pairing mechanism are suggested.

Source-reported materials — not catalogue approval

Similar papers