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It was recently shown that conventional phonon-electron interactions mayinduce a triplet pairing state in time-reversal invariant 3D Dirac semi -metals. Starting from the microscopic model of the isotropic Dirac semi-metal,the Ginzburg-Landau equations for the vector order parameter is derived usingthe Gor'kov technique. The collective modes including gapless Goldstone modes,and gapped Higgs modes of various polarizations are identified. They aresomewhat analogous to the modes in the B phase of He3, although in the presentcase quantitatively there is a pronouneced difference between longitudinal andtransverse components. The difference is caused by the vector nature of theorder parameter leading to two different coherence lengths or penetrationdepths. The system is predicted to be highly dissipative due to the Goldstonemodes. The time dependent Ginzburg - Landau model in the presence of externalfields is used to investigate some optical and magnetic properties of suchsuperconductors. The AC conductivity of a clean sample depends on theorientation of the order parameter. It is demonstrated that the differencebetween the penetration depths results in rotation of the polarization vectorof microwave passing a slab made of this material. The upper critical magneticfield H_{c2} was found. It turns out that at fields close to H_{c2} the orderparameter orients itself perpendicular to the field direction. In certain rangeof parameters the triplet superconducting phase persists at arbitrarily highmagnetic field like in some p wave superconductors.

Collective modes, AC response and magnetic properties of the 3D Dirac semi-metal in the triplet superconducting state