Type I superconductivity in Dirac materials

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.