  I study the effect of quantum and thermal phase fluctuations on the in-plane
and c-axis superfluid stiffness of layered d-wave superconductors. First, I
show that quantum phase fluctuations in the superconductor can be damped in the
presence of external screening of Coulomb interactions, and suggest an
experiment to test the importance of these fluctuations, by placing a metal in
close proximity to the superconductor to induce such screening. Second, I show
that a combination of quantum phase fluctuations and the linear temperature
dependence of the in-plane superfluid stiffness leads to a linear temperature
dependence of the c-axis penetration depth, below a temperature scale
determined by the magnitude of in-plane dissipation.
