Electron–phonon interaction and electronic correlations in transport through electrostatically and tunnel coupled quantum dots

We investigate two equivalent capacitively and tunnel coupled quantum dots, each coupled to its own pair of leads. Local Holstein type electron–phonon coupling at the dots is assumed. To study many-body effects we use the finite-U mean-field slave boson approach. For vanishing interdot interaction, weak e-ph coupling and finite tunneling, molecular orbital spin Kondo effects occur for single electron or single hole occupations. Phonons influence both correlations and tunneling and additionally they shift the energies of the dots. Depending on the dot energies and the strength of electron–phonon coupling, the system is occupied by a different number of electrons that effectively interact with each other repulsively or attractively leading to a number of different ground states of DQD. Among them are Kondo-like states with spin, orbital or charge correlations resulting from polaron cotunneling processes and states with magnetic intersite correlations. •Phonons induce various types of Kondo effects: spin, spin–orbital or charge-orbital resonances.•Impact of phonons on the competition of spin and isospin correlations with Kondo screening.•Switching of the sign of spin and isospin correlators due to electron–phonon coupling.