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 an S = ( N - 1)/2 impurity spin. For small enough interdot tunnel coupling, however, a two-stage Kondo effect takes place as the temperature is decreased. The spin 1/2 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/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 us to characterize the different strongly correlated regimes of the device.