Theory of the c-Axis Penetration Depth in the Cuprates

TL;DR

This paper explains the weak temperature dependence of the c-axis penetration depth in cuprates through a theory of incoherent quasiparticle hopping, reconciling it with in-plane d-wave pairing evidence.

Contribution

It introduces a theory based on incoherent quasiparticle hopping to unify c-axis penetration depth measurements with in-plane pairing symmetry in cuprates.

Findings

The c-axis penetration depth's temperature dependence can be explained by incoherent hopping.

The ratio of zero-temperature to finite-temperature penetration depth reveals c-axis transport behavior.

The theory links penetration depth measurements to c-axis resistivity and confinement phenomena.

Abstract

Recent measurements of the London penetration depth tensor in the cuprates find a weak temperature dependence along the c-direction which 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 CuO2 layers. By relating the calculated temperature dependence of the penetration depth \lambda_c(T) to the c-axis resistivity, we show how the measured ratio \lambda_c^2(0) / \lambda_c^2(T) can provide insight into the behavior of c-axis transport below Tc and the related issue of ``confinement.''