Penetration depth and the conductivity sum rule for a model with incoherent<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math>-axis coupling

Abstract

The conductivity sum rule for a one-band hopping model relates the integrated spectral weight of the real part of the conductivity to the average kinetic energy. For such a model, the superconducting penetration depth is therefore dependent upon both the change in the conductivity spectral weight and the change in kinetic energy between the normal and superconducting states. Here we examine the consequences of this for the $c$-axis penetration depth of a layered system in which the charge transfer perpendicular to the layers (along the $c$ axis) is mediated by interlayer impurity scattering.