Emergent superconductivity near the quantum critical point at zero magnetic and Kondo interactions in magnetic Kondo systems

Based on the Majorana-fermion representation of spins, we develop a gauge-invariant renormalized mean-field theory to investigate the Kondo magnetic systems. Here the Hamiltonian of the Kondo magnetic system is composed by nearest-neighbor magnetic interaction J_R for localized electrons, conduction electrons with Rashba spin-orbit interaction, and the Kondo interaction J_K. By solving the mean-field equations for different carrier density of the conduction electrons n_c, we obtain the complete phase diagram in the (J_R , J_K) space, where four general phases are exhibited as superconducting (SC) state, magnetic (ferromagnetic or anti-ferromagnetic) state, paramagnetic state or Fermi liquid. In particular, we find that near the quantum critical point at J_K = J_R =0, type of SC states proliferates and can be further classified as d-wave dominant, pure triplet p-wave, and extended s-wave with p-wave mixing SC phases. These SC phases are all connected to the quantum critical point, which provides a unique opportunity for investigating the interplay and transitions between different type of superconducting orders.