Abstract
We review the basic ideas of a renormalized perturbation theory which works directly in terms of fully dressed quasiparticles, and its application to the calculation of the current through a quantum dot both in equilibrium and non-equilibrium steady state conditions. The method is illustrated for the impurity Anderson model. We show how the relevant renormalized parameters can be deduced from a numerical renormalization group calculation, and also how they can be generalized to include an arbitrary magnetic field. In applying the method to electron transmission through quantum dot, we show how the zero field conductance can be expressed in terms of the renormalized parameters, and how asymptotically exact results at low bias voltages can be derived from the expansion to second order. The potential for the further application of this approach to this class of problems is assessed.
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References
L.H. Ryder, Quantum Field Theory (Cambridge University Press, Cambridge, 1996)
K. Wilson, Rev. Mod. Phys. 47, 773 (1975)
P.W. Anderson, Phys. Rev. 124, 41 (1961)
A.C. Hewson, Phys. Rev. Lett. 70, 4007 (1993)
A.C. Hewson, J. Phys.: Cond. Mat. 13, 10011 (2001)
A.C. Hewson, J. Phys.: Cond. Mat. 18, 1815 (2006)
H.R. Krishnamurthy, J.W. Wilkins, K.G. Wilson, Phys. Rev. B 21(3), 1003 (1980)
R. Bulla, T. Costi, T. Pruschke, Rev. Mod. Phys. 80, 395 (2008)
A.C. Hewson, A. Oguri, D. Meyer, Eur. Phys. J. B 40, 177 (2004)
A.C. Hewson, J. Phys. Soc. Japan 74, 8 (2005)
A.C. Hewson, J. Bauer, W. Koller, Phys. Rev. B 73, 045117 (2006)
J. Bauer, A.C. Hewson, Phys. Rev. B 76, 035119 (2007)
F.B. Anders, A. Schiller, Phys. Rev. Lett. 95, 196801 (2005)
F.B. Anders, Phys. Rev. Lett. 101, 066804 (2008)
F.B. Anders, J. Phys.: Cond. Mat. 20, 195216 (2008)
Y. Meir, N. Wingreen, Phys. Rev. Lett. 68, 2512 (1992)
L.V. Keldysh, Sov. Phys. JETP 20, 1018 (1965)
T. Rejec, A. Ramšak, Phys. Rev. B 68, 035342 (2003)
A. Oguri, A. Hewson, J. Phys. Soc. Japan 74, 988 (2005)
A. Oguri, Y. Nisikawa, A. Hewson, J. Phys. Soc. Japan 74, 2554 (2005)
T. Numata, Y. Nisikawa, A. Oguri, A. Hewson, Phys. Rev. B 80, 155330 (2009)
P. Mehta, N. Andrei, Phys. Rev. Lett. 96, 216802 (2006)
A. Oguri, Phys. Rev. B 64, 153305 (2001)
A. Oguri, J. Phys. Soc. Japan 74, 110 (2005)
M. Grobis, I.G. Rau, R.M. Potok, H. Shtrikman, D. Goldhaber-Gordon, Phys. Rev. Lett. 100, 246601 (2008)
J. Rincón, A. Aligia, K. Hallberg, Phys. Rev. B 79, 121301 (2009)
D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, M.A. Kastner, Nature 391, 156 (1998)
S.M. Cronenwett, T.H. Oosterkamp, L.P. Kouwenhoven, Science 281, 540 (1998)
A. Kogan, S. Amasha, D. Goldhaber-Gordon, G.Granger, M.A. Kastner, H. Shtrikman, Phys. Rev. Lett. 93, 166602 (2004)
A.C. Hewson, J. Bauer, A. Oguri, J. Phys.: Cond. Mat. 17, 5413 (2005)
T. Fujii, preprint: Arxiv:0807.4869 (cond-mat) (2008)
A. Gogolin, A. Komnik, Phys. Rev. Lett. 97, 016602 (2006)
Acknowledgements
We thank Y. Nisikawa for helpful discussions. This work is supported in part by an EPSRC grant (No. EP/GO32181/1) for one of us (ACH), and a JSPS Grant-in-Aid for Scientific Research (C) (Grant No. 20540319) for one of us (A.O.).
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Hewson, A.C., Oguri, A., Bauer, J. (2011). Renormalized Perturbation Approach to Electron Transport Through Quantum Dot. In: Bonca, J., Kruchinin, S. (eds) Physical Properties of Nanosystems. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0044-4_2
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DOI: https://doi.org/10.1007/978-94-007-0044-4_2
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