Non-equillibrium green’s functions method in matrix represenatation. 4. Quantum interference and dephasing

Authors: Kruglyak Yu.A., Kryzhanovskaya T.V.

Year: 2017

Issue: 21

Pages: 93-104


The following topics are discussed in the frame of the «bottom – up» approach of modern nanoelectronics: a super-brief but hopefully self-containing introduction to the Hamiltonian matrix whose eigenvalues tell us the allowed energy levels in the channel. However, the Hamiltonian describes an isolated channel and we can not talk about the steady-state resistance of an isolated chan-nel without bringing in the contacts and the battery connected across it. Non-equilibrium Green’s functions method in matrix presentation was initially formulated and applied to model transport problems for 1D and 2D conductors using a nearest neighbor orthogonal tight-binding model in the frame of the «bottom – up» approach of modern nanoelectronics. General method to account for electric contacts in Schrödinger equation to solve electron quantum transport problems is given. There are also discussed the elastic and spin dephasing modeling, account for non-coherent processes using Buttiker probe, 1D conductor with two and more scatterers, quantum interference, strong and weak localization, potential drop across scatterers, quantum oscillations in NEGF method without dephasing and with its account under phase and impulse relaxation regimes, destructive and constructive interference effects, four-component description of spin transport with account for dephasing and ending with discussion of quantum nature of classics including spin coherence and pseudo-spin formalism.

Tags: coherence; constructive interference; dephasing; destructive interference; impulse relaxation; molecular electronics; nanoelectronics; nanophysics; NEGF method; phase relaxation; pseudospin; quantum interference; spin coherence; spin transport; strong localization; weak localization; деструктивна інтерференція; деструктивна інтерференція; дефазировка; дефазировка; імпульсна релаксація; імпульсна релаксація; квантова інтерференція; квантова інтерференція; когерентність; когерентність; конструктивна інтерференція; конструктивна інтерференція; метод НРФГ; метод НРФГ; нанофизика; нанофизика; наноэлектроника; наноэлектроника; псевдоспин; псевдоспин; сильна локалізація; сильна локалізація; слабка локалізація; слабка локалізація; спинова когерентність; спинова когерентність; транспорт спинів; транспорт спинів; фазова релаксація; фазова релаксація


  1. Kruglyak Yu. A. Nanoelectronics “bottom – up”: Non-equilibrium Green function method, model transport prob-lems and quantum interference. Science-Rise, 2015, vol. 9, no. 2 (14), pp. 41–72. (In Russian)
  2. Buttiker M. Four-terminal phase-coherent conductance. Phys.Rev. Lett., 1986, vol. 57, p. 1761.
  3. Buttiker M. Symmetry of Electrical Conduction. IBM J. Res. Dev., 1988, vol. 32, no. 3, pp. 317–334.
  4. Golizadeh-Mojarad R., Datta S. Non-equilibrium Green’s function based model for dephasing in quantum transport. Phys. Rev. B., 2007, vol. 75, no. 8, pp. 081301/1–4.
  5. Kruglyak Yu. О., Strіkha M. V. Hall effect and measurement of electrochemical potentials within «bottom – up» approach. Sensor Electronics Microsys. Tech., 2014, vol. 11, no. 1, pp. 5–27. (In Ukrainian)
  6. Datta Supriyo. Lessons from Nanoelectronics: A New Per-spective on Transport. Hackensack, New Jersey: World Sci-entific Publishing Company, 2012. 473 р.
  7. Kruglyak Yu. O., Kruglyak N. E., Strіkha M. V. Lessons of Nanoelectronics. Spintronics in «Bottom – Up» Approach. Sensor Electronics Microsys. Tech., 2013, vol. 10, no. 2, pp. 5–35. (In Ukrainian)
  8. Kruglyak Yu. О., Strіkha M. V. Lessons of nanoelectronics: spin transport and quantum spin Hall effect by «bottom – up» approach. Sensor Electronics Microsys. Tech., 2014, vol. 11, no. 2, pp. 5–22. (In Ukrainian)
  9. Weber B., Mahapatra S., Ryu H., Lee S., Fuhrer A., Re-usch T. C. G., Thompson D. L., Lee W. C. T., Klimeck Gerhard, Hollenberg L. C. L., Simmons M. Y. Ohm’s Law Survives to the Atomic Scale. Science, 2012, vol. 335, pp. 64–67.
  10. Zurek W. H. Decoherence, Einselection and the Quantum Origins of the Classical. Rev. Mod. Phys., 2003, vol. 75, pp. 715–775.
  11. Kruglyak Yu. A. Graphene in the Landauer – Datta – Lund-strom Transport Model. ScienceRise, 2015, vol. 2, no. 2 (7), pp. 93–106. (In Russian)
  12. Abrikosov A. A., Gor’kov L. P., Dzyaloshinskiy I. E. Quan-tum field theoretical methods in statistical physics. Oxford: Pergamon Press, 1965. 365 p.
  13. Zubarev D. N. Two-time Green’s functions in statistical physics. Uspekhi v fizicheskikh naukakh – Advances in Physical Sciences, 1960, vol. LXXI, p. 71. (In Russian)
  14. Kruglyak Yu. A., Kvakush V. S., Dyadyusha G. G., Khil’chenko V. I. Metody vychisleniy v kvantovoy khimii [Methods of calculations in quantum chemistry]. Kiev: Nauk.Dumka, 1967.
  15. Glushkov A. V., Kruglyak Yu. A. Quasiparticle Lagrange method in theory of atoms and ions. In: Aktual’nye problemy spektroskopii [Actual Problems of Spectroscopy]. Moscow: AS USSR, 1985, p. 291. (In Russian)
  16. Kruglyak Yu. A., Glushkov A. V. Method of calculation of the chemical bond energies and lengths in a model of qua-sielectrons. Zhurnal fizicheskoy khimii ‒ Journ. of Phys. Chem., 1986, vol. 60, p. 1259. (In Russian)
  17. Glushkov A. V. New method for calculation of ionization potentials for molecules by Green’s functions method. Journ.Phys.Chem., 1992, vol. 66, p. 589.
  18. Glushkov A. V., Rusov V. D., Ambrosov S. V., Loboda A. V. Resonance State of Compound Superheavy Nucleus and Eppp in Heavy Nucleus Collisions. In:New Projects and Lines of Research in Nuclear Physics. Singapore: World Sci-entific, 2003, p. 126. (Eds: G. Fazio, F. Hanappe)
  19. Glushkov A. V. Relativistic and correlation effects in spectra of atomic systems. Odessa: Astroprint, 2006.
  20. Glushkov A. V., Lovett L., Khetselius O. Yu., Gurnit-skaya E. P., Dubrovskaya Yu. V., Loboda A. V. Generalized multiconfiguration model of decay of multipole giant reso-nances applied to analysis of reaction (m-n) on the nu-cleus 40Ca. Int.Journ. Modern Phys. A., 2009, vol. 24, p. 611.
  21. Glushkov A. V., Khetselius O. Y., Svinarenko A. A., Prepe-litsa G. P. Energy approach to atoms in a laser field and quan-tum dynamics with laser pulses of different shape. In: Coher-ence and Ultrashort Pulse Laser Emission. Intech, 2010, p. 159. (Ed.: Dr. F. J. Duarte)
  22. Khetselius O. Yu. Spectroscopy of cooperative electron-gamma-nuclear processes in heavy atoms: NEET effect. Journal of Phys.: C. Series., 2012, vol. 397, p. 012012.
Download full text (PDF)