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