Kondo effect and singlet-triplet splitting in coupled quantum dots in a magnetic field

We study the interplay between Kondo correlations and the singlet-triplet exchange splitting K between the two spins in a double quantum dot. We calculate the cotunneling current with elastic and inelastic contributions and its renormalization due to Kondo correlations, away and at the degeneracy point K=0. We show that these Kondo correlations induce pronounced peaks in the conductance G as a function of magnetic field B, inter-dot coupling $t_{\ab{H}}$, and temperature. The long-range part of the Coulomb interaction becomes visible due to Kondo correlations resulting in an additional peak in G vs. $t_{\ab{H}}$ with a strong B-field dependence. These conductance peaks thus provide direct experimental access to K, and thus to a crucial control parameter for spin-based qubits and entanglement