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Nonequilibrium Green’s Functions in the Atomic Representation and the Problem of Quantum Transport of Electrons Through Systems With Internal Degrees of Freedom

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Abstract

We develop the theory of quantum transport of electrons through systems with strong correlations between fermionic and internal spin degrees of freedom. The atomic representation for the Hamiltonian of a device and nonequilibrium Green’s functions constructed using the Hubbard operators allow overcoming difficulties in the perturbation theory encountered in the traditional approach because of a larger number of bare scattering amplitudes. Representing the matrix elements of effective interactions as a superposition of terms each of which is split in matrix indices, we obtain a simple method for solving systems of very many equations for nonequilibrium Green’s functions in the atomic representation. As a result, we obtain an expression describing the electron currents in a device one of whose sites is in tunnel coupling with the left contact and the other, with the right contact. We derive closed kinetic equations for the occupation numbers under conditions where the electron flow leads to significant renormalization of them.

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References

  1. C. F. Hirjibehedin, C. P. Lutz, and A. J. Heinrich, “Spin coupling in engineered atomic structures,” Science, 312, 1021–1024 (2006).

    Article  ADS  Google Scholar 

  2. H. Ueba, T. Mii, and S. G. Tikhodeev, “Theory of inelastic tunneling spectroscopy of a single molecule–competition between elastic and inelastic current,” Surface Science, 601, 5220–5225 (2007).

    Article  ADS  Google Scholar 

  3. P. I. Arseev and N. S. Maslova, “Electron–vibration interaction in tunneling processes through single molecules,” Phys. Usp., 53, 1151–1169 (2010).

    Article  ADS  Google Scholar 

  4. C. F. Hirjibehedin, C.-Y. Lin, A. F. Otte, M. Ternes, C. P. Lutz, B. A. Jones, and A. J. Heinrich, “Large magnetic anisotropy of a single atomic spin embedded in a surface molecular network,” Science, 317, 1199–1203 (2007).

    Article  ADS  Google Scholar 

  5. S. Loth, K. von Bergmann, M. Ternes, A. F. Otte, C. P. Lutz, and A. J. Heinrich, “Controlling the state of quantum spins with electric currents,” Nature Phys., 6, 340–344 (2010).

    Article  ADS  Google Scholar 

  6. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics [in Russian], Nauka, Moscow (1971); English transl., Consultants Bureau, New York, London (1974).

    Google Scholar 

  7. D. N. Zubarev, V. G. Morozov, and G. Röpke, Vol. 2, Relaxation and Hydrodynamic Processes, Vol. 1, Basic Concepts, Kinetic Theory, Akademie, Berlin (1997).

    MATH  Google Scholar 

  8. D. Rogovin and D. J. Scalapino, “Fluctuation phenomena in tunnel junctions,” Ann. Phys. (N. Y.), 86, 1–90 (1974).

    Article  ADS  Google Scholar 

  9. L. V. Keldysh, “Diagram technique for nonequilibrium processes,” JETP, 20, 1018–1026 (1965).

    MathSciNet  Google Scholar 

  10. R. O. Zaitsev, Introduction to Modern Kinetic Theory: A Set of Lectures [in Russian], KomKniga, Moscow (2006); English transl., Krasand, Moscow (2014).

    Google Scholar 

  11. P. I. Arseev, “On the nonequilibrium diagram technique: Derivation, some features, and applications,” Phys. Usp., 58, 1159–1205 (2015).

    Article  ADS  Google Scholar 

  12. R. O. Zaitsev, “Generalized diagram technique and spin waves in an anisotropic ferromagnet,” JETP, 41, 100–103 (1975); “Diagram technique and gas approximation in the Hubbard model,” JETP, 43, 574–579 (1976).

    ADS  Google Scholar 

  13. N. M. Plakida, L. Anton, S. Adam, and Gh. Adam, “Exchange and spin-fluctuation mechanisms of superconductivity in cuprates,” JETP, 97, 331–342 (2003).

    Article  ADS  Google Scholar 

  14. V. V. Val’kov, S. V. Aksenov, and E. A. Ulanov, “Effects of multiple reflection in the process of inelastic electron transport through an anisotropic magnetic atom,” JETP Lett., 98, 403–409 (2013).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Kirensky Institute of Physics, Siberian Branch, RAS, Krasnoyarsk, Russia

    V. V. Val’kov & S. V. Aksenov

Authors
  1. V. V. Val’kov
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  2. S. V. Aksenov
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Correspondence to V. V. Val’kov.

Additional information

This research was supported by the Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund (Grant Nos. 16-02-00073, 16-42-243056, 16-42-242036, and 17-42-240441) and in part (S. V. A.) by the Program for Governmental Support for Young Scientists and Candidates of Science (Grant No. MK-1398.2017.2).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 194, No. 2, pp. 277–294, February, 2018.

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Val’kov, V.V., Aksenov, S.V. Nonequilibrium Green’s Functions in the Atomic Representation and the Problem of Quantum Transport of Electrons Through Systems With Internal Degrees of Freedom. Theor Math Phys 194, 236–251 (2018). https://doi.org/10.1134/S0040577918020046

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  • DOI: https://doi.org/10.1134/S0040577918020046

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