Non-equilibrium singlet–triplet Kondo effect in carbon nanotubes

Abstract

1The Kondo-effect is a many-body phenomenon arising due to conduction electrons scattering off a localized spin 1 . Coherent spin-flip scattering off such a quantum impurity correlates the conduction electrons and at low temperature this leads to a zero-bias conductance anomaly 2,3 . This has become a common signature in bias-spectroscopy of single-electron transistors, observed in GaAs quantum dots 4,5,6,7,8,9 as well as in various single-molecule transistors 10,11,12,13,14,15 . While the zero-bias Kondo effect is well established it remains uncertain to what extent Kondo correlations persist in non-equilibrium situations where inelastic processes induce decoherence. Here we report on a pronounced conductance peak observed at finite bias-voltage in a carbon nanotube quantum dot in the spin singlet ground state. We explain this finite-bias conductance anomaly by a nonequilibrium Kondo-effect involving excitations into a spin triplet state. Excellent agreement between calculated and measured nonlinear conductance is obtained, thus strongly supporting the correlated nature of this nonequilibrium resonance.For quantum dots accommodating an odd number of electrons, a suppression of chargefluctuations in the Coulomb blockade regime leads to a local spin-1/2 degree of freedom and, when temperature is lowered through a characteristic Kondo-temperature T K , the Kondoeffect shows up as a zero-bias peak in the differential conductance. In a dot with an even number of electrons, the two electrons residing in the highest occupied level may either form a singlet or promote one electron to the next level to form a triplet, depending on the relative magnitude of the level splitting δ and the ferromagnetic intradot exchange energy J. For J > δ, the triplet state prevails and gives rise to a zero-bias Kondo peak 7,8 , but when δ > J the singlet state is lower in energy and no Kondo effect is expected in the linear conductance. Nevertheless, spin-flip tunneling becomes viable when the applied bias is large enough to induce transitions from singlet to triplet state. Such inter-lead exchange-tunneling may give rise to Kondo correlations and concomitant conductance peaks near V ∼ ±δ/e. However, since the tunneling involves excited states with a rather limited life-time, the question remains to what extend the coherence of such inelastic spin-flips and hence the Kondo-effect is maintained?In the context of a double-dot system, a qualitative description of a finite-bias Kondoeffect, leaving out decoherence and nonequilibrium effects, was given already in Ref.16 and 2 finite bias conductance peaks have already been observed in carbon nanotubes 11,14,17 as well as in GaAs quantum dots 8,9,18 . However, for lack of a quantitative theory for this nonequilibrium resonance no characterization of the phenomenon has yet been possible. As pointed out in Refs.19,20,21, a bias induced population of the excited state (here the triplet), may change a simple finite-bias cotunneling step into a cusp in the nonlinear conductance. Therefore, in order...

Quantum phase transition in a single-molecule quantum dot

“…This effect was recently elucidated on a carbon nanotube quantum dot in the singlet state [18]. As shown in the Supplementary Information, our results are consistent with this previous report.…”

“…While quantum critical phenomena related to Kondo screening have been attributed to the astonishing properties of many strongly correlated materials [10], a clear-cut observation in nanostructures of a screening-unscreening transition is still lacking. This is despite the intensive studies of singlettriplet Kondo effects measured through vertical quantum dots [11], GaAs lateral quantum dots under an applied magnetic field [12,13], or at zero magnetic field [14,15], carbon nanotubes [16,17,18,19], and double dot structures [20]. Indeed, the ability to observe a sharp quantum transition is limited either by the existence of two screening electronic channels (linked to conserved orbital quantum numbers), which generically give an avoided transition [21,22], or by relatively low Kondo temperatures, leading to the broad features observed in those experiments.…”

Single-molecule transport in three-terminal devices

“…At negative bias, the third derivative ( figure 5.4(c)) indicates the presence of three peaks. This evolution in a magnetic field, B, is consistent with inelastic cotunneling from a singlet ground state to an excited triplet state (see figure 5.4(b)) [73,74]. The splitting in each peak should be gμ B m s B with m s = ±1.…”

Noisy Kondo impurities

“…The possibility to design artificial controllable magnetic impurities in nanoscopic conductors has opened a path to study this many body phenomenon in unusual situations as compared to the initial one and, in particular, in out of equilibrium situations [8][9][10] . So far, measurements have focused on the average current.…”