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We review here some universal aspects of the physics of two-electronmolecular transistors in the absence of strong spin-orbit effects. Severalrecent quantum dots experiments have shown that an electrostatic backgate couldbe used to control the energy dispersion of magnetic levels. We discuss how thegenerically asymmetric coupling of the metallic contacts to two differentmolecular orbitals can indeed lead to a gate-tunable Hund's rule in thepresence of singlet and triplet states in the quantum dot. For gate voltagessuch that the singlet constitutes the (non-magnetic) ground state, onegenerally observes a suppression of low voltage transport, which can yet berestored in the form of enhanced cotunneling features at finite bias. Moreinterestingly, when the gate voltage is controlled to obtain the tripletconfiguration, spin S=1 Kondo anomalies appear at zero-bias, with non-Fermiliquid features related to the underscreening of a spin larger than 1/2.Finally, the small bare singlet-triplet splitting in our device allows tofine-tune with the gate between these two magnetic configurations, leading toan unscreening quantum phase transition. This transition occurs between thenon-magnetic singlet phase, where a two-stage Kondo effect occurs, and thetriplet phase, where the partially compensated (underscreened) moment is akinto a magnetically "ordered" state. These observations are put theoreticallyinto a consistent global picture by using new Numerical Renormalization Groupsimulations, taylored to capture sharp finie-voltage cotunneling featureswithin the Coulomb diamonds, together with complementary out-of-equilibriumdiagrammatic calculations on the two-orbital Anderson model. This work shouldshed further light on the complicated puzzle still raised by multi-orbitalextensions of the classic Kondo problem.

journal of physics. condensed matter

Universal transport signatures in two-electron molecular quantum dots:  gate-tunable Hund's rule, underscreened Kondo effect and quantum phase  transitions