Triplet superconductivity in 3D Dirac semimetal due to exchange interaction

Abstract

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 wide range of values of chemical potential $\mu $, the effective electron-electron coupling constant $\lambda $ and Debye energy $T_{D}$ demonstrates that when the exchange interaction is neglected the singlet always prevails, however in significant portions of the $\left( \mu ,\lambda ,T_{D}\right) $ 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 materials under consideration is the exchange (the Stoner term) characterized by constant $\lambda _{ex}$. We show that at values of $\lambda _{ex}$ much smaller then ones creating Stoner instability to ferromagnetism $\lambda _{ex}\sim 1$ the triplet pairing becomes energetically favored over the singlet ones for $\mu <T_{D}$% . The 3D quantum critical point at $\mu =0$ is considered in detail.