Triplet superconductivity in 3D Dirac semi-metal 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 µ, the effective electron-electron coupling constant λ and Debye energy TD demonstrates that when the exchange interaction is neglected the singlet always prevails, however in significant portions of the (µ, λ, TD) 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 λex. We show that at values of λex much smaller then ones creating Stoner instability to ferromagnetism λex ∼ 1 the triplet pairing becomes energetically favored over the singlet ones for µ < TD. The 3D quantum critical point at µ = 0 is considered in detail.

Magnetic impurities make superconductivity in 3D Dirac semi-metal triplet

“…Even within the BCS regime (SM), ∆ T /∆ S = sinh (0.35/λ) / sinh (0.5/λ). This is consistent with 1 only for quite large coupling and was studied in detail in [22].…”

Chiral universality class of normal-superconducting and exciton condensation transitions on surface of topological insulator

“…The local interaction term is not the most general one, but generalization to more exotic local cases (inter-valley [57] exchange spin-spin coupling [58]) is quite straightforward. The normal and anomalous Green's functions (consistent with the definition in Refs.…”

Collective modes of Weyl fermions with repulsive S-wave interaction*

“…For example, hightemperature d-wave superconductors, topological insulator, Dirac semi-metals, and Weyl semi-metals have been researched recently. [1][2][3][4][5] These materials possess an identical property of linear dispersion in the low-energy excitations near the Dirac or Weyl nodes.…”