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It was recently shown that conventional phonon-electron interactions inducetriplet pairing states in time-reversal invariant 3D Dirac semi - metalsprovided magnetic impurities or exchange interactions are strong enough?. Theorder parameter in this case is a vector field. Starting from the microscopicmodel of the isotropic Dirac semi-metal, the Ginzburg-Landau energy for thisfield is derived using the Gor'kov technique. It was found that the transversalcoherence length is much smaller than the longitudinal despite the isotropy.Several new features appear when an external field is applied. The Ginzburg -Landau model is used to investigate magnetic properties of suchsuperconductors. Using the small deviation method the magnetic penetrationdepth was found also to be vastly different for longitudinal and transversefluctuations. As a result the superconductor responds as type I to a transverseperturbation, while with respect to a longitudinal perturbation it behaves astype II. At large fields the order parameter orients itself perpendicular tothe field direction. The triplet superconductor persists at arbitrarily highmagnetic field (no upper critical magnetic field) like in some p wavesuperconductors.

Ginzburg - Landau theory of the triplet superconductivity in 3D Dirac semi-metal