Kondo effect in double quantum dots with ferromagnetic RKKY interaction.

We study Kondo effect in parallel-coupled double quantum dots with ferromagnetic Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction, by using the exact and nonperturbative hierarchical equations of motion approach. We construct the phase diagram in the parameter plane of the inter-dot coupling t and the ferromagnetic exchange interaction J (J  -  4t /U plane). Three different ground states, the Kondo singlet, spin singlet and S  =  1 Kondo, are determined in the diagram. We find the ferromagnetic coupling will raise the Kondo peak in the area of finite hopping t which is called 'J-enhanced Kondo effect'. Another enhancement of the Kondo effect by t ('t-enhanced Kondo effect') at J  =  0 is also presented. By checking the electron-electron interaction self-energy and magnetic susceptibility, we verify the ground state at large J is an under-screening Kondo state composed of a Fermi liquid with a residual spin 1/2, which is consistent with the 'singular Fermi liquid state' in the literature.