Topologically Protected Landau Level in the Vortex Lattice of a Weyl Superconductor

The question whether the mixed phase of a gapless superconductor can support a Landau level is a celebrated problem in the context of d-wave superconductivity, with a negative answer: the scattering of the subgap excitations (massless Dirac fermions) by the vortex lattice obscures the Landau level quantization. Here we show that the same question has a positive answer for a Weyl superconductor: the chirality of the Weyl fermions protects the zeroth Landau level by means of a topological index theorem. As a result, the heat conductance parallel to the magnetic field has the universal value G=12g0Φ/Φ0, with Φ as the magnetic flux through the system, Φ0 as the superconducting flux quantum, and g0 as the thermal conductance quantum.