Power-law Temperature Dependence of the Penetration Depth in a Topological Superconductor due to Surface States

We study the temperature dependence of the penetration depth in a 3D topological superconductor (TSC), incorporating the paramagnetic current due to the Majorana surface state. Bulk topological superconductors are predicted to host gapless 2D surface Majorana fluids, which are a promising platform for topological quantum computation. Here, we consider a model class DIII p-wave TSC and compute its response to an external magnetic field. Interestingly, in addition to the conventional London contribution to the Meissner effect coming from the bulk, our calculation shows that there is a non-trivial $T^{3}$ power law temperature dependence of the penetration depth due to the surface state in the low temperature limit. Our system is fully gapped in the bulk, and our result should be compared to bulk nodal superconductivity, which also exhibits power-law behavior. Our results imply that power-law temperature dependence of the penetration depth can be one indicator of topological superconductivity, in addition to the standard one-particle probes (STM, ARPES).