Angular dependence of the penetration depth in unconventional superconductors

We examine the Meissner state nonlinear electrodynamic effects on the field and angular dependence of the low temperature penetration depth, $\lambda$, of superconductors in several kinds of unconventional pairing states, with nodes or deep minima (``quasinodes'') in the energy gap. Our calculations are prompted by the fact that, for typical unconventional superconducting material parameters, the predicted size of these effects for $\lambda$ exceeds the available experimental precision for this quantity by a much larger factor than for others. We obtain expressions for the nonlinear component of the penetration depth, $\Delta\lambda$, for different two- and three- dimensional nodal or quasinodal structures. Each case has a characteristic signature as to its dependence on the size and orientation of the applied magnetic field. This shows that $\Delta\lambda$ measurements can be used to elucidate the nodal or quasinodal structure of the energy gap. For nodal lines we find that $\Delta\lambda$ is linear in the applied field, while the dependence is quadratic for point nodes. For layered materials with $\rm{YBa_2Cu_3O_{7-\delta}}$ (YBCO) type anisotropy, our results for the angular dependence of $\Delta\lambda$ differ greatly from those for tetragonal materials and are in agreement with experiment. For the two- and three- dimensional quasinodal cases, $\Delta\lambda$ is no longer proportional to a power of the field and the field and angular dependences are not separable, with a suppression of the overall signal as the node is filled in.