Measuring the London Penetration Depth in Aniso\-tropic Superconductors

We will show that by measuring the penetration depth in the conducting planes of an anisotropic superconductor and applying a magnetic field parallel to the conducting planes we can get rid of the signal coming from the vortices, and directly measure the London penetration depth, $\lambda_L$. Using a tunnel diode oscillator (TDO) in a dilution refrigerator, we have measured $\lambda_L$ verses magnetic field in CeCoIn$_5$ and found it to be linear, which is consistent with a d- wave order parameter. In the layered organic superconductor $\alpha$- (ET)$_2$HN$_4$Hg(SCN)$_4$, $\lambda_L$ verses magnetic field follows the shape predicted by BCS theory and an s-wave order parameter. The same measurement in $\kappa$-(ET)$_2$Cu(NCS)$_2$ is also consistent with an s-wave order parameter. The first two results are supported by other types of measurements, but the results for $\kappa$-(ET)$_2$Cu(NCS)$_2$ are puzzling because most other measurements suggest that there are nodes in its order parameter. We will discuss the possible reasons why $\lambda_L$ is not linear as a function of magnetic field in $\kappa$-(ET)$_2$Cu(NCS)$_2$. We will also discuss how the same measurements under pressure will sort help sort out the roles of impurities and inhomogeneity in these materials. In this context we will describe a new pressure cell we have designed for these TDO experiments, and our preliminary results. Work at Clark supported by NSF-DMR-0331272.