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Coulomb problem in nanostructures

Coulomb problem in nanostructures. E.M. Kazaryan, H.A. Sarkisyan Russian-Armenian University Yerevan State University. k. B A B. B A B. Types of nanostructures. 3D systems. 2D systems. A. B. 1D systems. 0D systems. The idea of size-quantisation. Kane’s disperssion law.

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Coulomb problem in nanostructures

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  1. Coulomb problem in nanostructures

  2. E.M. Kazaryan, H.A. Sarkisyan Russian-Armenian University Yerevan State University

  3. k B A B B A B Types of nanostructures 3D systems 2D systems

  4. A B 1D systems 0D systems

  5. The idea of size-quantisation

  6. Kane’s disperssion law

  7. E(k) G6 G8 Eg k 0 V1 G7 V2 V3 InS Experimental realization of InSb quantum dots K.D. Moiseev et al, Tech. Phys. Lett. (2007) InSb band structure

  8. h + e _ Two dimensional Kane’s excitonE.M. Kazaryan, L.S. Petrosyan, H.A. Sarkisyan, Physica E (2008). InSb Fig.11. Kane’s exciton in the InSb QW.

  9. Model of spherical InSb quantum dot

  10. Adiabatic approach

  11. - +

  12. (hh – e) – excitonic states

  13. Nanoscale rings GaInAs quantum rings (Lorke et all. Phys. Rev. Lett. (2000)). Chakraborty-Pietilainen model:

  14. R2 R1 R2 R1 Quantum ring L Confining potential Spherical nanolayer Cylindrical nanolayer R1 R2 Simple models layerednanostructures

  15. General character of results

  16. Importance! The importance of realization of that kind of geometry is in confirmation of Aaronov-Bom effect for bound states (the model of two-dimensional rotator in magnetic field).

  17. Two electrons in the quantum ring R1 R2

  18. R1 R2 On radial direction we ignore the Coulomb interaction and suppose that both electrons are in the ground radial state.

  19. R1 R2 R1 R2

  20. d

  21. Difference between approximated and exact functions of Coulomb interaction. Approximated (1) and exact (2) functions of Coulomb interaction.

  22. Angular equation

  23. Mathieu equation

  24. Two types of solution

  25. Oscillator energy approximation

  26. Oscillation character Harmonic Anharmonic Libration

  27. Harmonic R1 R2

  28. Anharmonic R1 R2

  29. Libration R1 R2

  30. Thank you for your attention!

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