Fundamental constraints for the mechanism of superconductivity in cuprates

Considerable progress has been made over the last decade in understanding the phenomenological properties of the cuprate high-Tc superconductors and in producing well characterized high quality materials. Nevertheless, the pairing mechanism itself remains controversial. We establish a criterion to test theories for layered superconductors relying on a substantial interlayer contribution. The criterion is based on the ratio of the interlayer contribution to the total superfluid density, which is traced back to the inverse squared effective mass anisotropy, 1/(1 + 2γ). γ can be measured rather accurately by various experimental techniques. It turns out that models relying on interlayer pairing cannot be considered as serious candidates for the mechanism of superconductivity in cuprate superconductors. PACS. 74.20.-z Theories and models of superconducting state – 74.20.Mn Nonconventional mechanisms One candidate mechanism to explain superconductivity in the cuprates is the interlayer tunneling (ILT) model proposed by P. W. Anderson and coworkers [1]-[3]. There, superconductivity is supposed to result primarily from an interlayer coupling mechanism. It has been argued [3,4], that the comparison of the measured interlayer magnetic penetration depth λc with the value determined from the ILT-model condensation energy, λ c , is a crucial test (c denotes the c-axis of the unit cell). Recent direct measurements of λc in Tl2Ba2CuO6+δ [5,6] and HgBa2CuO4+δ [7] make it unlikely that the present version of the ILT model is a serious candidate for the mechanism of superconductivity in cuprate superconductors. Indeed, λc turns out to be much larger than λ c [3]-[7]. However, it is important to recognize, that this approach is only applicable to theories, which can provide an estimate for λc. Here we introduce a more general measure for the ratio between the interlayer and total pairing interaction in the superconducting state. For this purpose the system is subjected to phase twists ki along three respective crystallographic axes i = a, b, c. In the presence of such a phase twist and in the limit ki → 0, the free energy density then reads as (see e.g. [8,9]) fi = kBT 2 Υik 2 i . (1) The helicity modulus Υi is given as Υi = Φ20 16π3λ i , (2) Correspondence to: J. M. Singer, Physikinstitut, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland, email: [email protected] 1 λ i = 16πh̄2ns MiΦo . (3) Φ0 is the flux quantum, λi the magnetic penetration depth, Mi denotes the effective pair mass appearing in the gradient term of an anisotropic Ginzburg-Landau action and ns is the superfluid number density. Imposing such twists of magnitude |ki| along the directions i = a, b, c, respectively, the ratio η = fc fa + fb + fc = Υc Υa + Υb + Υc