Interpretation of the temperature dependence of the electromagnetic penetration depth in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

The low-temperature behavior of the a-b plane penetration depth, ${\lambda }_{\mathit{a}\mathit{b}}$, is a probe of the pairing state in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. A group-theoretic analysis shows that in orthorhombic or tetragonal crystals all singlet pairing states other than ‘‘s wave’’ would lead to Δ${\lambda }_{\mathit{a}\mathit{b}}$(T)==${\lambda }_{\mathit{a}\mathit{b}}$(T)-${\lambda }_{\mathit{a}\mathit{b}}$(0)∼T. In contrast, for an isotropic system, there are combinations of singlet pairing states and field directions that would give rise to Δλ(T)∼${\mathit{T}}^3$. We reanalyze the surface impedance data of Fiory et al. [Phys. Rev. Lett. 61, 1419 (1988)], and show that these data exhibit neither a BCS temperature dependence nor a linear temperature dependence at low temperature, but instead follow Δ${\lambda }_{\mathit{a}\mathit{b}}$(T)∼${\mathit{T}}^2$. This behavior is probably not intrinsic, and possible explanations are discussed.