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Register a new userKondo Physics in Nanotubes: Magnetic-field dependence and singlet-triplet Kondo
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In a single-walled carbon nanotube, we observe the spin-1/2 Kondo effect. The energy of spin-resolved Kondo peaks is proportional to magnetic field at high fields, contrary to recent reports. At lower fields, the energy falls below this linear dependence, in qualitative agreement with theoretical expectations. For even electron occupancy, we observe a spin-1 Kondo effect due to the degeneracy of the triplet ground states. Tuning gate voltage within the same Coulomb diamond drives a transition to a singlet ground state. We also independently tune the energy difference between singlet and triplet states with a magnetic field. The Zeeman splitting thus measured confirms the value of the g-factor measured from the spin-1/2 Kondo feature.
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The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger-liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically-contacted single-wall nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far higher tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron number (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.
Within the framework of periodic asymmetric Anderson model for Kondo isoulators an effective singlet-triplet Hamiltonian with indirect antiferromagnetic f-f exchange interaction is introduced which allows to study analytically the dynamic magnetic susceptibilities of f-electrons. The approach allows to describe the three-level spin excitation spectrum with a specific dispersion in $YbB_{12}$. Distinctive feature of the consideration is the introduction of small radius singlet and triplet collective f-d excitations which at movement on a lattice form low - and high-energy spin bands.
The effect of magnetic impurities on the ballistic conductance of nanocontacts is, as suggested in recent work, amenable to ab initio study cite{naturemat}. Our method proceeds via a conventional density functional calculation of spin and symmetry dependent electron scattering phase shifts, followed by the subsequent numerical renormalization group solution of Anderson models -- whose ingredients and parameters are chosen so as to reproduce these phase shifts. We apply this method to investigate the Kondo zero bias anomalies that would be caused in the ballistic conductance of perfect metallic (4,4) and (8,8) single wall carbon nanotubes, ideally connected to leads at the two ends, by externally adsorbed Co and Fe adatoms. The different spin and electronic structure of these impurities are predicted to lead to a variety of Kondo temperatures, generally well below 10 K, and to interference between channels leading to Fano-like conductance minima at zero bias.
High quality single wall carbon nanotube quantum dots have been made showing both metallic and semiconducting behavior. Some of the devices are identified as small band gap semiconducting nanotubes with relatively high broad conductance oscillations for hole transport through the valence band and low conductance Coulomb blockade oscillations for electron transport through the conduction band. The transition between these regimes illustrates that transport evolves from being wave-like transmission known as Fabry-Perot interference to single particle-like tunneling of electrons or holes. In the intermediate regime four Coulomb blockade peaks appear in each Fabry-Perot resonance, which is interpreted as entering the SU(4) Kondo regime. A bias shift of opposite polarity for the Kondo resonances for one electron and one hole in a shell is in some cases observed.
We present transport measurements of the Kondo effect in a double quantum dot charged with only one or two electrons, respectively. For the one electron case we observe a surprising quasi-periodic oscillation of the Kondo conductance as a function of a small perpendicular magnetic field |B| lesssim 50mT. We discuss possible explanations of this effect and interpret it by means of a fine tuning of the energy mismatch of the single dot levels of the two quantum dots. The observed degree of control implies important consequences for applications in quantum information processing.
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