Triplet superconductivity in 3D Dirac semi-metal due to exchange interaction

Conventional phonon-electron interaction induces either triplet or one of two (degenerate) singlet pairing states in time reversal and inversion invariant 3D Dirac semi-metal. Investigation of the order parameters and energies of these states at zero temperature in a wide range of values of chemical potential μ, the effective electron-electron coupling constant λ and Debye energy T_D demonstrates that when the exchange interaction is neglected the singlet always prevails, however, in significant portions of the (μ, λ, T_D) parameter space the energy difference is very small. This means that interactions that are small, but discriminate between the spin singlet and the spin triplet, are important in order to determine the nature of the superconducting order there. The best candidate for such an interaction in the materials under consideration is the exchange (the Stoner term) characterized by constant λ_ex. We show that at values of λ_ex, much smaller than ones creating Stoner instability to ferromagnetism λ_ex ∼ 1, the triplet pairing becomes energetically favored over the singlet ones. The 3D quantum critical point at μ = 0 is considered in detail. This can be realized experimentally in optically trapped cold atom systems.