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Quantum Interference Effects on the Electronic Transmission Through Quantum Dot Molecules

  • Rodolfo H. Romero
  • Daniel A. Lovey
  • Diego Sebastian Acosta Coden
  • Sergio S. Gomez
Chapter
Part of the Lecture Notes in Nanoscale Science and Technology book series (LNNST, volume 14)

Abstract

The fabrication and control of devices at nanometric scale emphasizes the importance of quantum effects on the electronic motion in semiconductor heterostructures. The size of the systems through which the electrons move makes mandatory to take into account their wave-like character. As a consequence, the typical interference effects play an important role. In this chapter the noticeable Fano and Aharonov–Bohm effects in the transmission through a ring of quantum dots threaded by a magnetic flux will be discussed. They arise from the interference of the electron wave function when propagating along several transmission paths. The effects manifest themselves as peaks of high conductance and dips of cancellations of transmission along the ring. The control of the gate potentials applied to quantum dots and the magnetic field threading the ring allow one to tune the energies at which high and low transmissions occur.

Keywords

Magnetic Flux Green Function Energy Eigenvalue Transmission Function Fano Resonance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was partly supported by SGCyT (Universidad Nacional del Nordeste), National Agency ANPCYT and CONICET (Argentina) under grants PI F007/11, PICTO-UNNE 204/07 and PIP 11220090100654/2010.

References

  1. 1.
    Imry, Y.: Introduction to Mesoscopic Physics, 2nd edn. Oxford University Press, Oxford (2002)Google Scholar
  2. 2.
    Di Ventra, M.: Electrical Transport in Nanoscale Systems. Cambridge University Press, Cambridge (2008)CrossRefGoogle Scholar
  3. 3.
    Aronov, A.G., Shavin, Yu.V.: Magnetic flux effects in disordered conductors. Rev. Mod. Phys. 59, 755 (1987)CrossRefGoogle Scholar
  4. 4.
    Hod, O., Baer, R., Rabani, E.: Magnetoresistance of nanoscale molecular devices based on Aharonov-Bohm interferometry. J. Phys. Condens. Matter 20, 383201 (2008)CrossRefGoogle Scholar
  5. 5.
    Barnham, K., Vvedensky, D. (eds.): Low-Dimensional Semiconductor Structures. Fundamentals and Device Applications. Cambridge University Press, Cambridge (2001)Google Scholar
  6. 6.
    Ihn, T., Sigrist, M., Ensslin, K., Wegscheider, W., Reinwald, M.: Interference in a quantum dot molecule embedded in a ring interferometer. New J. Phys. 9, 111 (2007)CrossRefGoogle Scholar
  7. 7.
    Aharonov, Y., Bohm, D.: Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485 (1959)CrossRefGoogle Scholar
  8. 8.
    Nazarov, Y.V., Blanter, Y.M.: Quantum Transport - Introduction to Nanoscience. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  9. 9.
    Yacobi, A., Heiblum, M., Mahalu, D., Shtrikman, H.: Coherence and phase sensitive measurements in a quantum dot. Phys. Rev. Lett. 74, 4047 (1995)CrossRefGoogle Scholar
  10. 10.
    Sigrist, M., Fuhrer. A., Ihn, T., Ensslin, K., Ulloa, S.E., Wegscheider, W., Bichler, M.: Magnetic-field-dependent transmission phase of a double-dot system in a quantum ring. Phys. Rev. Lett. 93, 066802 (2004)Google Scholar
  11. 11.
    Hackenbroich, G.: Phase coherent transmission through interacting mesoscopic systems. Phys. Rep. 343, 463 (2001)CrossRefGoogle Scholar
  12. 12.
    Hod, O., Baer, R., Rabani, E.: Feasible nanometric magnetoresistance devices. J. Phys. Chem. B 108, 14807 (2004)CrossRefGoogle Scholar
  13. 13.
    Hod, O., Baer, R., Rabani, E.: Inelastic effects in Aharonov-Bohm molecular interferometers. Phys. Rev. Lett. 97, 266803 (2006)CrossRefGoogle Scholar
  14. 14.
    Sigrist, M., Ihn, T., Ensslin, K., Loss, D., Reinwald, M., Wegscheider, W.: Phase coherence in the inelastic cotunneling regime. Phys. Rev. Lett. 96, 036804 (2006)CrossRefGoogle Scholar
  15. 15.
    Büttiker, M., Imry, Y., Azbel, M.Ya.: Quantum oscillations in one-dimensional normal-metal rings. Phys. Rev. A 30, 1982 (1984)Google Scholar
  16. 16.
    Taniguchi, T., Büttker, M.: Friedel phases and phases of transmission amplitudes in quantum scattering systems. Phys. Rev. B 60, 13814 (1999)CrossRefGoogle Scholar
  17. 17.
    Levy Yeyati, A., Büttiker, M.: Scattering phases in quantum dots: An analysis based on lattice models. Phys. Rev. B 62, 7307 (2000)CrossRefGoogle Scholar
  18. 18.
    Ladrón de Guevara, M.L., Claro, F., Orellana, P.A.: Ghost Fano resonance in a double quantum dot molecule attached to leads. Phys. Rev. 67, 195335 (2003)Google Scholar
  19. 19.
    Ladrón de Guevara, M.L., Orellana, P.A.: Electronic transport through a parallel-coupled triple quantum dot molecule: Fano resonances and bound states in the continuum. Phys. Rev. 73, 205303 (2006)Google Scholar
  20. 20.
    Gómez, I., Domínguez-Adame, F., Orellana, P.: Fano-like resonances in three-quantum-dot Aharonov-Bohm rings. J. Phys. Condens. Matter 16, 1613 (2004)CrossRefGoogle Scholar
  21. 21.
    Hedin, E.R., Joe, Y.S., Satanin, A.M.: Resonance and phase shift in an open Aharonov-Bohm ring with an embedded quantum dot. J. Phys. Condens. Matter 21, 015303 (2009)CrossRefGoogle Scholar
  22. 22.
    An, X.-T., Liu, J.-J.: Aharonov-Bohm ring with a side-coupled quantum dot array as a spin switch. Appl. Phys. Lett. 96, 223508 (2010)CrossRefGoogle Scholar
  23. 23.
    Ladrón de Guevara, M.L., Lara, G.A., Orellana, P.A.: Quantum interference effects in two double quantum dots-molecules embedded in an Aharonov-Bohm ring. Phys. E 42, 1637 (2010)Google Scholar
  24. 24.
    Rai, D., Hod, O., Nitzan, A.: Circular currents in molecular wires. J. Phys. Chem. C 114, 20583 (2010)CrossRefGoogle Scholar
  25. 25.
    Rai, D., Hod, O., Nitzan, A.: Magnetic field control of the current through molecular ring junctions. J. Phys. Chem. Lett. 2, 2118 (2011)CrossRefGoogle Scholar
  26. 26.
    Akera, H.: Aharonov-Bohm effect and electron correlation in quantum dots. Phys. Rev. B 47, 6835 (1993)CrossRefGoogle Scholar
  27. 27.
    Izumida, W., Sakai, O., Shimizu, Y.: Many body effects on electron tunneling through quantum dots in an AB circuit. J. Phys. Soc. Jpn. 66, 717 (1997)CrossRefGoogle Scholar
  28. 28.
    Aharony, A., Entin-Wohlman, O.: Measuring the Kondo effect in the Aharonov-Bohm interferometer. Phys. Rev. B 72, 073311 (2005)CrossRefGoogle Scholar
  29. 29.
    Kang, K., Cho, S.Y.: Tunable molecular resonances of a double quantum dot Aharonov-Bohm interferometer. J. Phys. Condens. Matter 16, 117 (2004)CrossRefGoogle Scholar
  30. 30.
    Recher, P., Trauzettel, B., Rycerz, A., Blanter, Ya.M., Beenakker, C.W.J., Morpurgo, A.F.: Aharonov-Bohm effect and broken valley degeneracy in graphene rings. Phys. Rev. B 76, 235404 (2007)Google Scholar
  31. 31.
    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
  32. 32.
    Buchholz, S.S., Fischer, S.F., Kunze, U., Reuter, D., Wieck, A.D.: Nonlocal Aharonov-Bohm conductance oscillations in an asymmetric quantum ring. Appl. Phys. Lett. 94, 022107 (2009)CrossRefGoogle Scholar
  33. 33.
    Miyamoto, S., Moutanabbir, O., Ishikawa, T., Eto, M., Haller, E.E., Sawano, K., Shiraki, Y., Itoh, K.M.: Excitonic Aharonov-Bohm effect in isotopically pure70Ge/Si self-assembled type-II quantum dots. Phys. Rev. B 82, 073306 (2010)CrossRefGoogle Scholar
  34. 34.
    Neder, I., Heiblum, M., Levinson, Y., Mahalu, D., Umansky, V.: Unexpected behavior in a two-path electron interferometer. Phys. Rev. Lett. 96, 016804 (2006)CrossRefGoogle Scholar
  35. 35.
    Holleitner, A.W., Qina, H., Blicka, R.H., Eberlb, K., Kotthausa, J.P.: Aharonov-Bohm oscillations for charge transport through two parallel quantum dots. Phys. E 12, 774 (2002)CrossRefGoogle Scholar
  36. 36.
    Smirnov, D., Schmidt, H., Haug, R.J.: Aharonov-Bohm effect in an electron–hole graphene ring system. Appl. Phys. Lett. 100, 203114 (2012)CrossRefGoogle Scholar
  37. 37.
    Russo, S., Oostinga, J.B., Wehenkel, D., Heersche, H.B., Sobhani, S.S.: Observation of Aharonov-Bohm conductance oscillations in a graphene ring. Phys. Rev. B 77, 085413 (2008)CrossRefGoogle Scholar
  38. 38.
    Huefner, M., Molitor, F., Jacobsen, A., Pioda, A., Stampfer, C., Ensslin, K., Ihn, T.: The Aharonov-Bohm effect in a side-gated graphene ring. New J. Phys. 12, 043054 (2010)CrossRefGoogle Scholar
  39. 39.
    Yoo, J.S., Park, Y.W., Skákalová, V., Roth, S.: Shubnikov-de Haas and Aharonov Bohm effects in a graphene nanoring structure. Appl. Phys. Lett. 96, 143112 (2010)CrossRefGoogle Scholar
  40. 40.
    Hatano, T., Kubo, T., Tokura, Y., Amaha, S., Teraoka, S., Tarucha, S.: Aharonov-Bohm oscillations changed by indirect interdot tunneling via electrodes in parallel-coupled vertical double quantum dots. Phys. Rev. Lett. 106, 076801 (2011)CrossRefGoogle Scholar
  41. 41.
    Sigrist, M., Ihn, T., Ensslina, K., Reinwald, M., Wegscheider, W.: Is inelastic cotunneling phase coherent? J. Appl. Phys. 101, 081701 (2007)CrossRefGoogle Scholar
  42. 42.
    Mühle, A., Wegscheider, W., Haug, R.J.: Quantum dots formed in a GaAs/AlGaAs quantum ring. Appl. Phys. Lett. 92, 013126 (2008)CrossRefGoogle Scholar
  43. 43.
    Neder, I., Ofek, N., Chung, Y., Heiblum, M., Mahalu, D., Umansky, V.: Interference between two indistinguishable electrons from independent sources. Nature 448, 333 (2007)CrossRefGoogle Scholar
  44. 44.
    Fano, U.: Effects of configuration interactions of intensities and phase shifts. Phys. Rev. 124, 1866 (1961)CrossRefGoogle Scholar
  45. 45.
    Kobayashi, K., Aikawa, H., Katsumoto, S., Iye, Y.: Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer. Phys. Rev. Lett. 88, 256806 (2002)CrossRefGoogle Scholar
  46. 46.
    Fuhrer, A., Brusheim, P., Ihn, T., Sigrist, M., Ensslin, K., Wegscheider, W., Bichler, M.: Fano effect in a quantum-ring-quantum-dot system with tunable coupling. Phys. Rev. B 73, 205326 (2006)CrossRefGoogle Scholar
  47. 47.
    Miroshnichenko, A.E., Flach, S., Kivshar, Y.S.: Fano resonances in nanoscale structures. Rev. Mod. Phys. 82, 2257 (2010) and references thereinGoogle Scholar
  48. 48.
    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
  49. 49.
    Löwdin, P.O.: Studies in perturbation theory. IV. Solution of eigenvalue problem by projection operator formalism. J. Math. Phys. 3, 969 (1962)Google Scholar
  50. 50.
    Lovey, D.A., Gomez, S.S., Romero, R.H.: Transmission through a quantum dot molecule embedded in an Aharonov-Bohm interferometer. J. Phys. Condens. Matter 23, 425303 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Rodolfo H. Romero
    • 1
  • Daniel A. Lovey
    • 1
  • Diego Sebastian Acosta Coden
    • 1
  • Sergio S. Gomez
    • 1
  1. 1.Facultad de Ciencias Exactas y Naturales y AgrimensuraInstituto de Modelado e Innovación Tecnológica (CONICET-UNNE)CorrientesArgentina

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