Magnetic properties of type-I and type-II Weyl semimetals in the superconducting state

Superconductivity was observed in certain range of pressure and chemical composition in Weyl semimetals of both type I and type II (when the Dirac cone tilt parameter κ>1). Magnetic properties of these superconductors are studied on the basis of microscopic phonon-mediated pairing model. The Ginzburg-Landau effective theory for the order parameter is derived using the Gorkov approach and used to determine anisotropic coherence length, the penetration depth determining the Abrikosov parameter for a layered material and applied to recent extensive experiments on MoTe2. It is found that superconductivity is of second kind near the topological transition at κ=1. For a larger tilt parameter, superconductivity becomes first kind. For κ<1, the Abrikosov parameter also tends to be reduced, often crossing over to the first kind. For the superconductors of the second kind, the dependence of critical fields Hc2 and Hc1 on the tilt parameter κ (governed by pressure) is compared with the experiments. Strength of thermal fluctuations is estimated and it is found that they are strong enough to cause Abrikosov vortex lattice melting near Hc2. The melting line is calculated and is consistent with experiments provided the fluctuations are three dimensional in the type-I phase (large pressure) and two dimensional in the type-II phase (small pressure).