Circular transmission resonances and magnetic field effects in a ring of quantum dots connected to external leads in the meta-configuration

  • Eric R. HedinEmail author
  • Arkady M. Satanin
  • Yong S. Joe


The transmission and the circular transmission are investigated for a ring of quantum dots (in a benzene-type configuration) connected to external leads in the meta-configuration. A computational method utilizing the tight-binding approximation to the Schrödinger equation is used to solve for the transmission probabilities as a function of the electron energy and external magnetic flux. The flux dependence is incorporated into the model using a standard procedure involving the Aharonov–Bohm effect. The positions of the transmission zeros and poles in the complex energy plane, and their possible interference with or even complete cancellation of each other, are shown to correlate with the amplitude and structure of the circular transmission resonances. Large-amplitude resonances of the circular transmission are found to occur when two poles of the transmission are separated along the imaginary axis. These resonances demonstrate a high degree of flux sensitivity at specific energy values and flux ranges. A small change in flux causes the orientation of the resonance poles in the complex energy plane to rotate parallel to the real energy axis, resulting in a concurrent decrease in the circular transmission amplitude. The flux-dependent interference between the transmission poles and zeros in the complex energy plane leads to a decrease of the circular transmission resonance amplitudes. The circular transmission and its corresponding current–voltage characteristic provide more information related to the external flux than can be obtained from the normal transmission alone.


Quantum dot ring Magnetic flux Circular current Resonances Complex energy plane 



The authors acknowledge that the research of A.M.S. is supported in part by the Ministry of Education of the Russian Federation (project #3.3026.2017), and the RFBR (grants 16-07-01012 and 18-07-01206).


  1. 1.
    Joachim, C., Gimzewski, J.K., Aviram, A.: Electronics using hybrid-molecular and mono-molecular devices. Nature 408, 541 (2000)CrossRefGoogle Scholar
  2. 2.
    Rai, D., Hod, O., Nitzan, A.: Magnetic fields effects on the electronic conduction properties of molecular ring structures. Phys. Rev. B 85, 155440 (2012)CrossRefGoogle Scholar
  3. 3.
    Rai, D., Hod, O., Nitzan, A.: Circular currents in molecular wires. J. Phys. Chem. C 114, 20583 (2010)CrossRefGoogle Scholar
  4. 4.
    Solomon, G.C., Andrews, D.Q., Hansen, T., Goldsmith, R.H., Wasielewski, M.R., Van Duyne, R.P., Ratner, M.A.: Understanding quantum interference in coherent molecular conduction. J. Chem. Phys. 129, 054701 (2008)CrossRefGoogle Scholar
  5. 5.
    Chen, F., Tao, N.J.: Electron transport in single molecules: from benzene to graphene. Acc. Chem. Phys. 42, 429 (2009)CrossRefGoogle Scholar
  6. 6.
    Naumis, G.G., Terrones, M., Terrones, H., Gaggero-Sager, L.M.: Design of graphene electronic devices using nanoribbons of different widths. Appl. Phys. Lett. 95, 182104 (2009)CrossRefGoogle Scholar
  7. 7.
    Hansen, T., Solomon, G.C., Andrews, D.Q., Ratner, M.A.: Interfering pathways in benzene: an analytical treatment. J. Chem. Phys. 131, 194704 (2009)CrossRefGoogle Scholar
  8. 8.
    Adak, O., Korytár, R., Joe, A.Y., Evers, F., Venkataraman, L.: Impact of electrode density of states on transport through pyridine-linked single molecule junctions. Nano Lett. 15, 3716 (2015)CrossRefGoogle Scholar
  9. 9.
    Hod, O., Baer, R., Rabani, E.: Feasible nanometric magnetoresistance devices. J. Phys. Chem. B 108, 14807 (2004)CrossRefGoogle Scholar
  10. 10.
    Hedin, E.R., Joe, Y.S., Satanin, A.M.: Sharpened Aharonov–Bohm oscillations near resonance in a balanced ring with double quantum dots. J. Comput. Electron. 7, 280 (2008)CrossRefGoogle Scholar
  11. 11.
    Patra, Moumita, Maiti, Santanu K.: Modulation of circular current and associated magnetic field in a molecular junction: a new approach. Sci. Rep. 7, 43343 (2017)CrossRefGoogle Scholar
  12. 12.
    Maiti, S.K.: Externally controlled local magnetic field in a conducting mesoscopic ring coupled to a quantum wire. J. Appl. Phys. 117, 024306-1–024306-7 (2015)CrossRefGoogle Scholar
  13. 13.
    Malakooti, S., Hedin, E.R., Joe, Y.S.: Tight-binding approach to strain-dependent DNA electronics. J. Appl. Phys. 114, 014701 (2013)CrossRefGoogle Scholar
  14. 14.
    Tsuji, N., Takajo, S., Aoki, H.: Large orbital magnetic moments in carbon nanotubes generated by resonant transport. Phys. Rev. B 75, 153406 (2007)CrossRefGoogle Scholar
  15. 15.
    Deo, P.S., Jayannavar, A.M.: Quantum waveguide transport in serial stub and loop structures. Phys. Rev. B 50, 11629 (1994)CrossRefGoogle Scholar
  16. 16.
    Cohen, G., Hod, O., Rabani, E.: Constructing spin interference devices from nanometric rings. Phys. Rev. B 76, 235120–235133 (2007)CrossRefGoogle Scholar
  17. 17.
    Datta, S.: Quantum Transport: Atom to Transistor. Cambridge University Press, New York (2005)CrossRefzbMATHGoogle Scholar
  18. 18.
    Jayannavar, A.M., Singha Deo, P.: Persistent currents in the presence of a transport current. Phys. Rev. B 51, 10175 (1995)CrossRefGoogle Scholar

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Authors and Affiliations

  • Eric R. Hedin
    • 1
  • Arkady M. Satanin
    • 2
    • 3
  • Yong S. Joe
    • 4
  1. 1.Department of Chemistry, Physics & EngineeringBiola UniversityLa MiradaUSA
  2. 2.Dukhov All-Russia Research Institute of Automatics (VNIIA)MoscowRussia
  3. 3.Russia National Research University Higher School of Economics (MIEM)MoscowRussia
  4. 4.Department of Physics and Astronomy, Center for Computational NanoscienceBall State UniversityMuncieUSA

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