Recent development of nanotechnology has enabled us to study the correlated transport in mesoscopic devices. Kondo effect in a quantum dot is a fascinating example. In this year, our group has investigated the shot noise for the Kondo effect in a quantum dot.

Recently shot noise in the Kondo regime has been studied. Especially in Refs.[1,2], the Fermi-liquid nature has been reexamined. They have considered the "backscattering current" I_b which expresses a reduction from the perfect transmission for the π/2 phase shift. It has been shown that the Fano factor F_b=S/2eI_b results in a universal fractional value 5/3 up to V³. This universal feature has stimulated further studies. A shot-noise measurement has been reported on 5/3[3]. In the context of the full counting statistics[4] this result has been reproduced.

We have extended this result into any strength of Coulomb interaction by using the renormalization perturbation theory (RPT). Concerning shot noise, we have used the new formula of shot noise proposed in our recent study[5]. There, we have an expression of differential conductance: G=βS/4 -β S_h/4 where S is the current-current correlation function, and S_h is the non-trivial current-charge correlation function and β=1/k_BT. We have called it the nonequilibrium Kubo formula. This is written into S_h=S-4k_BTG. At zero temperature S_h equals the conventional shot noise S. In the linear response regime S_h is proven to vanish, and the Nyquist-Johnson relation is reproduced. Furthermore in noninteracting systems S⁰-4k_BTG⁰ expresses the known result of the shot noise. Therefore we have proposed that S_h gives a definition of shot noise at any temperature in correlated systems. Thus theoretically calculated S_h can be compared with S-4k_BTG. using S and G measured in experiments. Therefore, the nonequilibrium Kubo formula enables us to address shot noise at any temperature in correlated systems[6]. We have applied this approach to the shot noise in a quantum dot. Then, the Fano factor has been estimated F_b =1+4(R-1)²/[ 1+5(R-1) ]² where R is the Wilson ratio. Using limiting values of the Wilson ratio R=2 in the Kondo limit, F_b=5/3 is correctly derived. Therefore this expression gives the general expression in any Coulomb interaction strength[6].

References

• E. Sela, Y. Oreg, F von Oppen, and J. Koch, Phys. Rev. Lett. 97, 086601 (2006).
• A. Golub, Phys. Rev. B 73, 233310 (2006); ibid. 75, 155313 (2007).
• O. Zarchin, M. Zaffalon, M. Heiblum, D. Mahalu, and V. Umansky, Phys. Rev. B 77, 241303(R) (2008).
• A. O. Gogolin and A. Komnik, Phys. Rev. Lett. 97, 016602 (2006).
• T. Fujii, J. Phys. Soc. Jpn. 76, 044709 (2007).
• T. Fujii, submitted to J. Phys. Soc. Jpn..

Authors

• T. Fujii