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

Abstract

Abstract. We review here some universal aspects of the physics of two-electron molecular transistors in the absence of strong spin-orbit effects. Several recent quantum dots experiments have shown that an electrostatic backgate could be used to control the energy dispersion of magnetic levels. We discuss how the generically asymmetric coupling of the metallic contacts to two different molecular orbitals can indeed lead to a gate-tunable Hund's rule in the presence of singlet and triplet states in the quantum dot. For gate voltages such that the singlet constitutes the (non-magnetic) ground state, one generally observes a suppression of low voltage transport, which can yet be restored in the form of enhanced cotunneling features at finite bias. More interestingly, when the gate voltage is controlled to obtain the triplet configuration, spin S = 1 Kondo anomalies appear at zero-bias, with non-Fermi liquid features related to the underscreening of a spin larger than 1/2. Finally, the small bare singlet-triplet splitting in our device allows to fine-tune with the gate between these two magnetic configurations, leading to an unscreening quantum phase transition. This transition occurs between the non-magnetic singlet phase, where a two-stage Kondo effect occurs, and the triplet phase, where the partially compensated (underscreened) moment is akin to a magnetically "ordered" state. These observations are put theoretically into a consistent global picture by using new Numerical Renormalization Group simulations, taylored to capture sharp finie-voltage cotunneling features within the Coulomb diamonds, together with complementary outof-equilibrium diagrammatic calculations on the two-orbital Anderson model. This work should shed further light on the complicated puzzle still raised by multi-orbital extensions of the classic Kondo problem.

Non-Fermi-Liquid Behavior in Transport Through Co-Doped Au Chains

“…This is nearly the ideal value 2G 0 expected for perfect transmission with two channels. However, with increasing temperature the conductance falls more rapidly than for a usual Kondo model, reflecting the physics of the UK model [3][4][5][6][7]. We have obtained an excellent fit of the NRG data below T K , using a phenomenological expression proposed for one-channel UK models [6,38] (see fit [Parks 2010] in Fig.…”

“…In spite of the large effect of correlations, these systems are Fermi liquids where, for example, the conductance has the expected behavior GðTÞ ' Gð0Þ À aT 2 for T ( T K , with T K the Kondo temperature and a some constant. More recently, the underscreened Kondo (UK) effect, leading to singular Fermi liquid physics [3,4] has been observed, and quantum phase transitions (QPTs) involving partially Kondo screened spin-1 molecular states were induced by externally controlled parameters [5][6][7].The overscreened Kondo effect, the simplest manifestation of which is the two-channel Kondo (2CK) model, is even more interesting because inelastic scattering persists even at vanishing temperatures and excitation energies. Therefore, the system is a non-Fermi liquid, exhibiting fascinating low-energy properties [8][9][10].…”

“…In spite of the large effect of correlations, these systems are Fermi liquids where, for example, the conductance has the expected behavior GðTÞ ' Gð0Þ À aT 2 for T ( T K , with T K the Kondo temperature and a some constant. More recently, the underscreened Kondo (UK) effect, leading to singular Fermi liquid physics [3,4] has been observed, and quantum phase transitions (QPTs) involving partially Kondo screened spin-1 molecular states were induced by externally controlled parameters [5][6][7].…”

Kondo behavior and conductance through 3d impurities in gold chains doped with oxygen

“…In the last years there has been a great amount of experiments in electronic transport through semiconducting [1,2,3,4,5,6,7] and molecular [8,9,10,11,12] quantum dots (QDs), in which manifestations of the Kondo effect were observed. In addition, experiments with mechanically controllable break junctions made possible to create one-dimensional atomic chains of several elements [13,14,15], and the conductance of noble-metal nanowires with transition-metals impurities has been measured using point-contact techniques [16,17].…”

“…The underscreened Kondo effect and quantum phase transitions involving partially Kondo screened spin-1 molecular states were observed in transport experiments by changing externally controlled parameters [10,11]. On the other hand, a system consisting in a Co atom inside a Au chain, in which the symmetry is reduced to four-fold by connecting it to appropriate leads has been proposed as a possible realization of the overscreened Kondo model [23,24,25].…”