Climbing the Entropy Barrier: Driving the Single- towards the Multichannel Kondo Effect by a Weak Coulomb Blockade of the Leads

We study a model proposed recently in which a small quantum dot is coupled symmetrically to several large quantum dots characterized by a charging energy E_c. Even if E_c is much smaller than the Kondo temperature T_K, the long-ranged interactions destabilize the single-channel Kondo effect and induce a flow towards a multi-channel Kondo fixed point associated with a rise of the impurity entropy with decreasing temperature. Such an ``uphill flow'' implies a negative impurity specific heat, in contrast to all systems with local interactions. An exact solution found for a large number of channels allows us to capture this physics and to predict transport properties.Comment: 4 pages, 3 figures. Recent references and new title added in published versio

A brief review of recent advances on the Mott transition: unconventional transport, spectral weight transfers, and critical behaviour

Strongly correlated metals close to the Mott transition display unusual transport regimes, together with large spectral weight transfers in optics and photoemission. We briefly review the theoretical understanding of these effects, based on the dynamical mean-field theory, and emphasize the key role played by the two energy scales associated with quasiparticle coherence scale and with the Mott gap. Recent experimental results on two-dimensional organic compounds and transition metal oxides are considered in this perspective. The liquid-gas critical behaviour at the Mott critical endpoint is also discussed. Transport calculations using the numerical renormalization group are presented.Comment: Review article. 9 pages, 5 figures. Proceedings of the Vth International Conference on Crystalline Organic Metals, Superconductors and Magnets (ISCOM 2003

Impact of capacitance and tunneling asymmetries on Coulomb blockade edges and Kondo peaks in non-equilibrium transport through molecular quantum dots

We investigate theorerically the non-equilibrium transport through a molecular quantum dot as a function of gate and bias voltage, taking into account the typical situation in molecular electronics. In this respect, our study includes asymmetries both in the capacitances and tunneling rates to the source and drain electrodes, as well as an infinitely large charging energy on the molecule. Our calculations are based on the out-of-equilibrium Non-Crossing-Approximation (NCA), which is a reliable technique in the regime under consideration. We find that Coulomb blockade edges and Kondo peaks display strong renormalization in their width and intensity as a function of these asymmetries, and that basic expectations from Coulomb blockade theory must be taken with care in general, expecially when Kondo physics is at play. In order to help comparison of theory to experiments, we also propose a simple phenomenological model which reproduces semi-quantitatively the Coulomb blockade edges that were numerically computed from the NCA in all regimes of parameters.Comment: 9 pages, 8 figure

Interplay of Kondo effect and strong spin-orbit coupling in multi-hole ultraclean carbon nanotubes

We report on cotunneling spectroscopy magnetoconductance measurements of multi-hole ultraclean carbon nanotube quantum dots in the SU(4) Kondo regime with strong spin-orbit coupling. Successive shells show a gradual weakening of the Kondo effect with respect to the spin-orbital splittings, leading to an evolution from SU(4) to SU(2) symmetry with a suppressed conductance at half shell filling. The extracted energy level spectrum, overally consistent with negligible disorder in the nanotube, shows in the half filled case large renormalizations due to Coulombian effects.Comment: 5 pages, 4 figures, 1 supplementary fil

The Kondo effect in bosonic spin liquids

In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature. In contrast, impurity moments coupled to spin-1 bulk bosons, such as triplet excitations in paramagnets, are only partially screened, even at the bulk quantum critical point. We argue that this difference is not due to the quantum statistics of the host particles but instead related to the structure of the impurity-host coupling, by demonstrating that frustrated magnets with bosonic spinon excitations can display a bosonic version of the Kondo effect. However, the Bose statistics of the bulk implies distinct behavior, such as a weak-coupling impurity quantum phase transition, and perfect screening for a range of impurity spin values. We discuss implications of our results for the compound Cs2CuCl4, as well as possible extensions to multicomponent bosonic gases.Comment: 4 pages, 3 figures. The weak coupling RG flow was corrected and expanded in last versio

Gate-tuned high frequency response of carbon nanotube Josephson junctions

Carbon nanotube (CNT) Josephson junctions in the open quantum dot limit exhibit superconducting switching currents which can be controlled with a gate electrode. Shapiro voltage steps can be observed under radiofrequency current excitations, with a damping of the phase dynamics that strongly depends on the gate voltage. These measurements are described by a standard RCSJ model showing that the switching currents from the superconducting to the normal state are close to the critical current of the junction. The effective dynamical capacitance of the nanotube junction is found to be strongly gate-dependent, suggesting a diffusive contact of the nanotube.Comment: 14 pages, 8 figure

Singular dynamics and pseudogap formation in the underscreened Kondo impurity and Kondo lattice models

We study a generalization of the Kondo model in which the impurity spin is represented by Abrikosov fermions in a rotation group SU(P) larger than the SU(N) group associated to the spin of the conduction electrons, thereby forcing the single electronic bath to underscreen the localized moment. We demonstrate how to formulate a controlled large N limit preserving the property of underscreening, and which can be seen as a ``dual'' theory of the multichannel large N equations usually associated to overscreening. Due to the anomalous scattering on the uncompensated degrees of freedom, the Fermi liquid description of the electronic fluid is invalidated, with the logarithmic singularities known to occur in the S=1 SU(2) Kondo impurity model being replaced by continuous power laws at N=\infty. The present technique can be extended to tackle the related underscreened Kondo lattice model in the large N limit. We discover the occurence of an insulating pseudogap regime in place of the expected renormalized metallic phase of the fully screened case, preventing the establishement of coherence over the lattice. This work and the recent observation of a similar weakly insulating behavior on transport in CeCuAs_2 should give momentum for further studies of underscreened impurity models on the lattice.Comment: 9 pages, 3 figures. Several modifications in published version, including new title, further details on the interpretation of the formalism and possible experimental connection

Slave-rotor mean field theories of strongly correlated systems and the Mott transition in finite dimensions

The multiorbital Hubbard model is expressed in terms of quantum phase variables (``slave rotors'') conjugate to the local charge, and of auxiliary fermions, providing an economical representation of the Hilbert space of strongly correlated systems. When the phase variables are treated in a local mean-field manner, similar results to the dynamical mean-field theory are obtained, namely a Brinkman-Rice transition at commensurate fillings together with a ``preformed'' Mott gap in the single-particle density of states. The slave- rotor formalism allows to go beyond the local description and take into account spatial correlations, following an analogy to the superfluid-insulator transition of bosonic systems. We find that the divergence of the effective mass at the metal- insulator transition is suppressed by short range magnetic correlations in finite-dimensional systems. Furthermore, the strict separation of energy scales between the Fermi- liquid coherence scale and the Mott gap found in the local picture, holds only approximately in finite dimensions, due to the existence of low-energy collective modes related to zero-sound.Comment: 16 pages, 12 figure

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

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 out-of-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.Comment: Review article. 16 pages, 17 figures. Minor corrections and extra references added in V