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.

Three BCS superconductors Sa, Sb, and S and two short normal regions Na and Nb in a three-terminal SaNaSNb Sb setup provide a source of nonlocal quartets spatially separated as two correlated pairs in Sa and Sb, if the distance between the interfaces Na S and SNb is comparable to the coherence length in S. Low-temperature dc transport of nonlocal quartets from S to Sa and Sb can occur in equilibrium, and also if Sa and Sb are biased at opposite voltages. At higher temperatures, thermal excitations result in correlated current fluctuations which depend on the superconducting phases Φa and Φb in Sa and Sb. Phase-sensitive entanglement is obtained at zero temperature if Na and Nb are replaced by discrete levels.

15 pages, 11 figuresInternational audiencePredictions are established for linear differential current-current cross-correlations dSab/dV in a symmetrically biased three-terminal normal metal-superconductor-normal metal (NSN) device. Highly transparent contacts turn out to be especially interesting because they feature positive dSab/dV. At high transparency, processes based on Crossed Andreev Reflection (CAR) contribute only negligibly to the current and to dSab/dV. Under these circumstances, current-current cross-correlations can be plausibly interpreted as a coherent coupling between the two NS interfaces in the form of synchronized Andreev and inverse Andreev reflections, corresponding to the process where a pair of electron-like quasi-particles and a pair of hole-like quasi-particles arrive from the normal electrodes and annihilate in the superconductor. Hence, positive dSab/dV does not automatically imply CAR. For tunnel contacts, dSab/dV is positive because of CAR. In between these two extremities, at intermediate transparencies, dSab/dV is negative because both processes which cause positive correlations, occur only with small amplitude. We use scattering theory to obtain analytic expressions for current and noise, and microscopic calculation using a tight binding model in order to obtain a clear interpretation of the physical processes

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Numerical renormalization group (NRG) calculations of quantum impurity models, based on a logarithmic discretization in energy of electronic or bosonic Hamiltonians, provide a powerful tool to describe physics involving widely separated energy scales, as typically encountered in nanostructures and strongly correlated materials. This main advantage of the NRG was however considered a drawback for resolving sharp spectral features at finite energy, such as dissipative atomic peaks. Surprisingly, we find a bunching of many-body levels in NRG spectra near dissipative resonances, and exploit this by combining the widely-used Oliveira's z-trick, using an averaging over few discrete NRG spectra, with an optimized frequency-dependent broadening parameter b(ω). This strategy offers a tremendous gain in computational power and extracts all the needed information from the raw NRG data without a priori knowledge of the various energy scales at play. As an application we investigate with high precision the crossover from coherent to incoherent dynamics in the spin boson model. PACS numbers:A general hallmark of many-particle interaction, as found in a variety of condensed matter systems such as nanostructures and strongly correlated materials, lies in the presence of several energy scales, possibly widely separated from each other due to renormalization and dynamical effects. Two well-studied examples found in electronic systems concern the Kondo effect for magnetic impurities in metals and Fermi liquids in proximity to a Mott insulating phase, two instances where low-energy quasiparticles emerge below a typical temperature which is quite reduced from the bare Fermi energy 1 . These lowlying excitations do however coexist with higher energy atomic levels, also broadened and displaced in a strong manner from their bare atomistic values due to the dissipation brought by the electronic environment. Such complex physical effects, taking place on a broad range of energies, entail great practical difficulties for most direct numerical approaches. These are partially lifted using Wilson's original idea of the logarithmic discretization 2,3 , as implemented in numerical renormalization group calculations (see Ref. 4 for a recent review). This technique has been improved in the last twenty years to calculate static and dynamic quantities both for fermionic 5 and bosonic quantum impurity models 6 . Important practical applications until now involve the calculation of transport in the Kondo regime for Kondo alloys and artificial quantum dots 7 , as well as the accurate description of the zero-temperature Mott transition by combining NRG 8 with Dynamical Mean Field Theory (DMFT) 9 . More generally, exponentially small energy scales are also found in the vicinity of quantum critical points 10 , so that impurity models provide a simplified testbed for the theory of quantum critical phenomena 11 . Again the NRG is the ideal technique for studying such impurity quantum phase transitions 4 , with potential implications for artificial nanostru...

We show that scanning gate microscopy can be used for probing electron-electron interactions inside a nanostructure. We assume a simple model made of two noninteracting strips attached to an interacting nanosystem. In one of the strips, the electrostatic potential can be locally varied by a charged tip. This change induces corrections upon the nanosystem Hartree-Fock self-energies which enhance the fringes spaced by half the Fermi wavelength in the images giving the quantum conductance as a function of the tip position.

Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a numerical renormalization group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a nonperturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single static defect.

Abstract. A nano-system in which electrons interact and in contact with Fermi leads gives rise to an effective one-body scattering which depends on the presence of other scatterers in the attached leads. This non local effect is a pure many-body effect that one neglects when one takes non interacting models for describing quantum transport. This enhances the non-local character of the quantum conductance by exchange interactions of a type similar to the RKKY-interaction between local magnetic moments. A theoretical study of this effect is given assuming the Hartree-Fock approximation for spinless fermions of Fermi momentum kF in an infinite chain embedding two scatterers separated by a segment of length Lc. The fermions interact only inside the two scatterers. The dependence of one scatterer onto the other exhibits oscillations of period π/kF which decay as 1/Lc and which are suppressed when Lc exceeds the thermal length LT.