  Superconductivity of the second kind was observed in many 3D Weyl and Dirac
semi-metals. However in PdT e2, superconductivity is clearly of the first kind.
This is very rare in Dirac semi - metals, but is expected in clean conventional
metallic superconductors with 3D parabolic dispersion relation. The conduction
bands in this material exhibit the linear (Dirac) dispersion only along two
directions, while in the third direction the dispersion is parabolic. Therefore
the "hybrid" Dirac-parabolic material is intermediate between the two extremes.
A microscopic pairing theory is derived for arbitrary tilt parameter of the 2D
cone and used to determine anisotropic coherence lengths, the penetration
depths and applied to recent extensive experiments. Magnetic properties of
these superconductors are then studied on the basis of microscopically derived
Ginzburg - Landau effective theory for the order parameter.
