Using nonequilibrium Green functions and several complementary many-body approximations we calculate shot noise and spin dependent conductance in carbon nanotube semiconducting quantum dot in spin-orbital Kondo regime. We point out on the possibility of reaching giant values of tunnel magnetoresistance in this range and discuss a prospect of its gate control. We also analyze the influence of symmetry breaking perturbations on the shot noise with special emphasis on spin dependent effects. The gate and bias dependencies of noise Fano factors influenced by magnetic field, polarization of electrodes and spin-flip processes are presented.

Based on ab-initio calculations we discuss Kondo effect due to Co adatom on graphene zigzag nanoribbon. Co atom located at hollow site behaves as spin S = 1/2 impurity with d xz and d yz orbitals contributing to magnetic moment. Dynamical correlations are analyzed with the use of complementary approximations: mean field slave boson approach, noncrossing approximation and equation of motion method. The impact of interplay between spin and orbital degrees of freedom together with the effect of peculiarities of electronic and magnetic structure of nanoribbon on many-body resonances is examined. PACS numbers: 73.22.Pr, 73.23.-b, 75.20.Hr, 85.75.-d arXiv:1307.5872v1 [cond-mat.mes-hall]

Abstract. The linear response transport properties of carbon nanotube quantum dot in the strongly correlated regime are discussed. The finite-U mean field slave boson approach is used to study many-body effects. Magnetic field can rebuilt Kondo correlations, which are destroyed by the effect of spin-orbit interaction or valley mixing. Apart from the field induced revivals of SU(2) Kondo effects of different types: spin, valley or spin-valley, also more exotic phenomena appear, such as SU(3) Kondo effect. Threefold degeneracy occurs due to the effective intervalley exchange induced by short-range part of Coulomb interaction or due to the intershell mixing. In narrow gap nanotubes the full spin-orbital degeneracy might be recovered in the absence of magnetic field opening the condition for a formation of SU(4) Kondo resonance.

The coherent spin dependent transport through a set of two capacitively coupled quantum dots placed in a magnetic field is considered within the equation of motion method. The magnetic field breaks the spin degeneracy. For special choices of gate voltages the dot levels are tuned to resonance and the orbital Kondo effect results. For different Zeemann splittings at the dots the Kondo resonance can be formed for only one spin channel. In this case the system operates as an efficient spin filter.

Strong electron correlations and interference effects are discussed in parallel-coupled single-level and orbitally doubly degenerate quantum dots. The finite-U mean-field slave boson approach is used to study many-body effects. The analysis is carried out in a wide range of parameter space including both atomic-like and molecular-like Kondo regimes and taking into account various perturbations, like interdot tunneling, interdot interaction, mixing of the electrode channels and exchange interaction. We also discuss the influence of singularities of electronic structure and the impact of polarization of electrodes. Special attention is paid to potential spintronic applications of these systems showing how current polarization can be controlled by adjusting interference conditions and correlations by gate voltage. Simple proposals of double dot spin valve and bipolar electrically tunable spin filter are presented.

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Strong electron correlations and interference effects are discussed in capacitively coupled side attached and embedded quantum dots. The finite -U mean field slave boson approach is used to study many-body effects. In the linear range the many-body resonances exhibit SU(4) Kondo or Kondo-Fano like character and their properties in the corresponding arms are close to the properties of embedded or T-shape double dot systems respectively. Breaking of the spin symmetry in one of the arms or in both allows for the formation of many-body resonances of SU(3) or SU(2) symmetries in the linear range.