Ferromagnetic and underscreened Kondo behavior in quantum dot arrays

We analyze the low energy properties of a device with $N+1$ quantum dots in a star configuration. A central quantum dot is tunnel coupled to source and drain electrodes and to $N$ quantum dots. Extending previous results for the $N=2$ case we show that, in the appropriate parameter regime, the low energy Hamiltonian of the system is a ferromagnetic Kondo model for a $S=(N-1)\mathrm{/}2$ impurity spin. For small enough interdot tunnel coupling, however, a two-stage Kondo effect takes place as the temperature is decreased. The spin $1\mathrm{/}2$ in the central quantum dot is Kondo screened first and at lower temperatures the antiferromagnetic coupling to the side coupled quantum dots leads to an underscreened $S=N\mathrm{/}2$ Kondo effect. We present numerical results for the thermodynamic and spectral properties of the system which show a singular behavior at low temperatures and allow to characterize the different strongly correlated regimes of the device.