Theory of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math>-axis penetration depth in the cuprates

Abstract

Recent measurements of the London penetration-depth tensor in the cuprates find a weak temperature dependence along the $c$ direction that is seemingly inconsistent with evidence for $d$-wave pairing deduced from in-plane measurements. We demonstrate in this paper that these disparate results are not in contradiction, but can be explained within a theory based on incoherent quasiparticle hopping between the Cu${\mathrm{O}}_{2}$ layers. By relating the calculated temperature dependence of the penetration depth ${\ensuremath{\lambda}}_{c}(T)$ to the $c$-axis resistivity, we show how the measured ratio $\frac{{\ensuremath{\lambda}}_{c}^{2}(0)}{{\ensuremath{\lambda}}_{c}^{2}(T)}$ can provide insight into the behavior of $c$-axis transport below ${T}_{c}$ and the related issue of "confinement."