Kondo Effects in Carbon Nanotubes: From SU(4) to SU(2) symmetry

Korea Institute for Advanced Study, Sŏul, Seoul, South Korea
Physical Review B (Impact Factor: 3.74). 08/2006; 74(20). DOI: 10.1103/PhysRevB.74.205119
Source: arXiv


We study the Kondo effect in a single-electron transistor device realized in a single-wall carbon nanotube. The K-K' double orbital degeneracy of a nanotube, which originates from the peculiar two-dimensional band structure of graphene, plays the role of a pseudo-spin. Screening of this pseudo-spin, together with the real spin, can result in an SU(4) Kondo effect at low temperatures. For such an exotic Kondo effect to arise, it is crucial that this orbital quantum number is conserved during tunneling. Experimentally, this conservation is not obvious and some mixing in the orbital channel may occur. Here we investigate in detail the role of mixing and asymmetry in the tunneling coupling and analyze how different Kondo effects, from the SU(4) symmetry to a two-level SU(2) symmetry, emerge depending on the mixing and/or asymmetry. We use four different theoretical approaches to address both the linear and non-linear conductance for different values of the external magnetic field. Our results point out clearly the experimental conditions to observe exclusively SU(4) Kondo physics. Although we focus on nanotube quantum dots, our results also apply to vertical quantum dots. We also mention that a finite amount of orbital mixing corresponds, in the pseudospin language, to having non-collinear leads with respect to the orbital ''magnetization'' axis which defines the two pseudospin orientations in the nanotube quantum dot. In this sense, some of our results are also relevant to the problem of a Kondo quantum dot coupled to non-collinear ferromagnetic leads. Comment: 17 pages, 15 figures; Updated references, fig13 corrected, typos corrected; to appear in Phys. Rev. B

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Available from: Ramon Aguado, Nov 16, 2012
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    • "Adapted from ((Jarillo-Herrero et al., 2005)). observations of spin-orbital Kondo effect in CNTs (Grove-Rasmussen et al., 2007; Wu et al., 2009) and several interesting theoretical papers on SU(4) Kondo problem have been published very recently (Büsser & Martins, 2007; Choi et al., 2005; Galpin et al., 2006; Lim et al., 2006; Lipí nski & Krychowski, 2005; Mizumo et al., 2009). The unusual strongly correlated Fermi liquid state, where spin and orbital degrees of freedom are totally entangled is interesting for quantum computing and storage technology. "

    Full-text · Chapter · Jul 2011
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    • "These valley-state flip resonances are associated with different processes based on their evolution with magnetic field. The processes which involve both a valley flip and a spin flip are expected to shift to energies ±∆ ± g * µ B B, while those without a spin-flip stay at energies ±∆[14,25]. We only seem to observe the resonances at ±∆, i.e. the valley-state flip resonances without spin flip. "
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    ABSTRACT: The Kondo effect has been observed in a single gate-tunable atom. The measurement device consists of a single As dopant incorporated in a silicon nanostructure. The atomic orbitals of the dopant are tunable by the gate electric field. When they are tuned such that the ground state of the atomic system becomes a (nearly) degenerate superposition of two of the silicon valleys, an exotic and hitherto unobserved valley Kondo effect appears. Together with the "regular" spin Kondo, the tunable valley Kondo effect allows for reversible electrical control over the symmetry of the Kondo ground state from an SU(2) to an SU(4) configuration.
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    ABSTRACT: Cette thèse a pour objet l'étude du transport électronique dans les nanotubes de carbone monoparois par l'intermédiaire des fluctuations du courant. L'étude se place dans le cadre de la physique mésoscopique dans des conducteurs balistiques. Dans ce type de conducteur, plusieurs régimes diff´erents peuvent apparaître : blocage de Coulomb, transport modulé par les interférences quantiques, effet Kondo. Nous avons étudié les fluctuations du courant dans un régime d'interféromètre de type Fabry-Pérot électronique qui se présente comme une situation id´eale afin de sonder le régime où l'effet des interactions est faible. Les fluctuations du courant ont été analysées dans le formalisme de Landauer-Büttiker et nous obtenons une bonne correspondance entre la théorie et l'expérience. Nous avons ainsi observé la suppression du bruit dans les régimes de transmission unitaire et, par le biais des données combinées de la conductance et du bruit, nous avons pu déterminer les transmissions pour des canaux de conduction non dégénérés. Par ailleurs, le régime de l'effet Kondo a fait l'objet d'une étude dans laquelle nous avons observé des comportements universels dans la conductance et le bruit. Nous avons ajusté ces différentes grandeurs avec une théorie de bosons esclaves de champ moyen. Finalement, nous avons étudié une configuration de type Hanbury Brown et Twiss : un nanotube monoparoi sur lequel nous avons déposé un multiparoi qui nous sert de sonde afin d'injecter des électrons sur le conducteur.
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