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Full Counting Statistics for SU(N) Impurity Anderson Model

Kato Group

The distribution of current flowing through nanoscale-objects such as quantum dots has useful information on how electrons are transmitted. For example, the current noise (the second moment of the current distribution) calculated for the SU(2) Kondo dot revealed that the non-equilibrium backscattering current is composed of two types of electron transfer due to single quasiparticles and pairs of quasiparticles, carrying charge e and 2e, respectively[1]. In other words, in addition to usual ‘one-by-one’ electron transfer, ‘synchronized’ transfer by paired electrons may occur due to strong Coulomb repulsions. The same result was obtained in a clearer way by direct calculation of the current distribution function in general formalism of the full counting statistics (FCS)[2].

Fig. 1. (a) A Fano factor defined as a ratio between current noise and backscattering current, which is recognized as an average charge of transfer carriers. Inset: A schematic figure of an SU(N) Anderson impurity model. (b) Cross correlation between currents through different levels.

In the present work[3], we extend the FCS approach to multiorbital Kondo dots, which can be experimentally realized in vertical dots, carbon nanotube, and double dots. We consider an SU(N) impurity Anderson model (see the inset of Figure1(a)) as a prototype model for examining multiorbital effects. This model assumes N-degenerate quantum states (including spin degrees of freedom) at an impurity site: the Kondo dots with one orbital and two degenerate orbitals corresponds to N=2 and 4, respectively. We theoretically find that current correlation through different orbitals provides a wealth of information if the system is in the non-equilibrium Kondo regime.

We calculate the Fano factor (the ratio between noise and backscattering current) for an SU(N) Anderson model, which can be recognized as an effective charge of carriers transmitting through a dot. The result for N=2 and 4 is shown in Fig. 1 (a). As the Coulomb repulsion increases, the Fano factor changes from 1 to 5/3 for N=2, and to 3/2 for N=4. This result suggests that ‘synchronized’ quasiparticle transfer with two electrons starts to work under strong Coulomb repulsions. The ‘synchronized’ quasiparticle transfer can be observed also in the current cross-correlation shown in Fig. 1 (b), where correlation between currents through different orbitals is induced by the Coulomb repulsion. As the number of degenerate orbitals increases, proportion of ‘synchronized’ quasiparticle transfer observed in the Fano factor is reduced, but remains a sufficiently large value for N=4. We note that cross correlation in the SU(4) case can be measured experimentally without any spin-dependent current detection, whereas cross correlation in the SU(2) case can also be measured in double-dot systems if a spin degree of freedom is replaced by a pseudo-spin assigned to electron configuration.

In summary, we have examined current correlation in an SU(N) Anderson model, and have shown that electron correlation between different orbitals, recognized as an ‘orbital-singlet’, produces current correlations for different orbitals, giving a direct measure of this synchronized transfer. Our calculation indicates that precise description of this effect needs careful consideration based on a non-equilibrium version of the local Fermi liquid theory. We expect that our result will be examined through current cross-correlation measurement in orbital-degenerate nanoscale objects.


References
  • [1] E. Sela, Y. Oreg, F. von Oppen, and J. Koch, Phys. Rev. Lett. 97, 086601 (2006).
  • [2] A. O. Gogolin and K. Komnik, Phys. Rev. Lett. 97, 016602 (2006).
  • [3] R. Sakano, A. Oguri, T. Kato, and S. Tarucha, Phys. Rev. B 83, 241301(R) (2011).
Authors
  • R. Sakano, A. Oguria, T. Kato, and S. Taruchab
  • aOsaka City University
  • bUniversity of Tokyo