Electron Tunneling Excitation of a Coupled Two Impurity System



Kondo effects in individual atoms, molecular magnets or quantum dots have received a lot of attention. Systems with two units, like double quantum dots or two atoms, have also attracted some attention due to the interplay between the possible coupling between the spins of the two components and the Kondo effect of each unit. Moreover, the tunneling spectroscopy across one or several magnetic atoms deposited on a metal surface has also been analyzed and shown to present properties associated with spin-flip processes and Kondo resonances. In this paper we analyze the electron tunneling excitations created in a dimer case, assuming that each unit (atom or quantum well) has spin \(\frac{1}{2}\). In our approach, the basic Hamiltonian includes the spin-metal hybridization as well as the spin-spin interaction; then, its basic properties are analyzed by means of a Green’s function formalism combined with an Equation of Motion method. We present results showing the tunneling differential conductance as a function of the different parameters of the problem and the limits for which spin-flip processes and/or Kondo resonances appear.



ECG acknowledges financial support by CONICET through Grant No. PIP-201101-00621 and U.N.L. through CAI+D grants. FF acknowledges support from the Spanish Ministerio de Economía y Competitividad (MINECO) under project MAT2014-59966-R, and through the ‘María de Maeztu’ Programme for Units of Excellence in R&D (MDM-2014-0377).


  1. 1.
    C.F. Hirjibehedin, C.P. Lutz, A.J. Heinrich, Science 312(5776), 1021 (2006).  https://doi.org/10.1126/science.1125398
  2. 2.
    C.F. Hirjibehedin, C.Y. Lin, A.F. Otte, M. Ternes, C.P. Lutz, B.A. Jones, A.J. Heinrich, Science 317(5842), 1199 (2007).  https://doi.org/10.1126/science.1146110
  3. 3.
    A.F. Otte, M. Ternes, K. von Bergmann, S. Loth, H. Brune, C.P. Lutz, C.F. Hirjibehedin, A.J. Heinrich, Nat. Phys. 4(11), 847 (2008).  https://doi.org/10.1038/nphys1072
  4. 4.
    R. Bulla, T.A. Costi, T. Pruschke, Rev. Mod. Phys. 80, 395 (2008).  https://doi.org/10.1103/RevModPhys.80.395
  5. 5.
    A.F. Otte, M. Ternes, S. Loth, C.P. Lutz, C.F. Hirjibehedin, A.J. Heinrich, Phys. Rev. Lett. 103, 107203 (2009).  https://doi.org/10.1103/PhysRevLett.103.107203
  6. 6.
    H. Brune, P. Gambardella, Surf. Sci. 603(10), 1812 (2009).  https://doi.org/10.1016/j.susc.2008.11.055. (Special Issue of Surface Science dedicated to Prof. Dr. Dr. h.c. mult. Gerhard Ertl, Nobel-Laureate in Chemistry 2007)
  7. 7.
    A. Spinelli, M. Gerrits, R. Toskovic, B. Bryant, M. Ternes, A.F. Otte, 6, 10046 (2015).  https://doi.org/10.1038/ncomms10046
  8. 8.
    B. Bryant, A. Spinelli, J.J.T. Wagenaar, M. Gerrits, A.F. Otte, Phys. Rev. Lett. 111, 127203 (2013).  https://doi.org/10.1103/PhysRevLett.111.127203
  9. 9.
    B. Bryant, R. Toskovic, A. Ferrón, J.L. Lado, A. Spinelli, J. Fernández-Rossier, A.F. Otte, Nano Lett. 15(10), 6542 (2015).  https://doi.org/10.1021/acs.nanolett.5b02200
  10. 10.
    M. Persson, Phys. Rev. Lett. 103, 050801 (2009).  https://doi.org/10.1103/PhysRevLett.103.050801
  11. 11.
    R. Žitko, T. Pruschke, New J. Phys. 12(6), 063040 (2010).  https://doi.org/10.1088/1367-2630/12/6/063040
  12. 12.
    J. Fernández-Rossier, Phys. Rev. Lett. 102, 256802 (2009).  https://doi.org/10.1103/PhysRevLett.102.256802
  13. 13.
    F. Delgado, J. Fernández-Rossier, Phys. Rev. B 82, 134414 (2010).  https://doi.org/10.1103/PhysRevB.82.134414
  14. 14.
    B. Sothmann, J. König, New J. Phys. 12(8), 083028 (2010).  https://doi.org/10.1088/1367-2630/12/8/083028
  15. 15.
    J. Fransson, O. Eriksson, A.V. Balatsky, Phys. Rev. B 81, 115454 (2010).  https://doi.org/10.1103/PhysRevB.81.115454
  16. 16.
    M. Ternes, New J. Phys. 17(6), 063016 (2015).  https://doi.org/10.1088/1367-2630/17/6/063016
  17. 17.
    N. Lorente, J.P. Gauyacq, Phys. Rev. Lett. 103, 176601 (2009).  https://doi.org/10.1103/PhysRevLett.103.176601
  18. 18.
    J. Kondo, Prog. Theor. Phys. 32(1), 37 (1964).  https://doi.org/10.1143/PTP.32.37
  19. 19.
    E.C. Goldberg, F. Flores, J. Phys.: Cond. Matter 25(22), 225001 (2013).  https://doi.org/10.1088/0953-8984/25/22/225001
  20. 20.
    E.C. Goldberg, F. Flores, Phys. Rev. B 91, 165408 (2015).  https://doi.org/10.1103/PhysRevB.91.165408
  21. 21.
    E.C. Goldberg, F. Flores, Inelastic electron scattering in aggregates of transition metal atoms on metal surfaces. Phys. Rev. B 96, 115439 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    E.C. Goldberg, F. Flores, Phys. Rev. B 77, 125121 (2008).  https://doi.org/10.1103/PhysRevB.77.125121
  23. 23.
    N.H. March, Electron Density Theory of Atoms and Molecules (Academic Press, New York, 1992)Google Scholar
  24. 24.
    A. Ayuela, N.H. March, Int. J. Quantum Chem. 110(15), 2725 (2010).  https://doi.org/10.1002/qua.22764
  25. 25.
    F. Flores, N.H. March, I.D. Moore, Surf. Sci. 69(1), 133 (1977).  https://doi.org/10.1016/0039-6028(77)90165-0

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Física Teórica de la Materia Condensada and IFIMACUniversidad Autónoma de MadridMadridSpain
  2. 2.Instituto de Física del Litoral (CONICET-UNL)Santa FeArgentina
  3. 3.Departamento Ingeniería de Materiales, Facultad de Ingeniería QuímicaUniversidad Nacional del LitoralSanta FeArgentina

Personalised recommendations