1. Spherical and cylindrical nanolayers: electronic states, quantum transitions Hayk Sarkisyan Russian-Armenian (Slavonic) University Yerevan State University

2. The idea of size-quantisation

3. Some geometries of quantum dots

5. Fulerens and nanotubes

6. Simple models of layered systemsZ O R1 R2 X Y Z O
Spherical layer QD
Cylindrical layer QD

8. GaInAs quantum rings Lorke et al (Phys. Rev. Lett. 84, 2223 (2000)).
Fig. 1.
GaInAs quantum rings Lorke et al (Phys. Rev. Lett. 84, 2223 (2000)).
250250 нм2.

9. Bound structures of quantum layer
Fig. 2.
Bound structures of quantum layer

10. Chakraborty-Pietilainen model (Phys. Rev. Lett. 84, 2223 (2000))
Fig. 3.
Chakraborty-Pietilainen model (Phys. Rev. Lett. 84, 2223 (2000))
Fig. 4.
Smorodinsky-Winternitz model
(Yadernaya fizika 4, 625 (1966)).

11. Difference between potentials profiles: 2 1
Fig. 5.
Difference between potentials profiles:
1. Chakraborty-Pietilainen model,
2. Smorodinsky-Winternitz model

12. 1. Parameters of quantum ring
Experimental data (Lorke et al - Phys. Rev. Lett. 84, 2223 (2000))
quantum ring – InAs
coating – GaAs
inner radius – 10 nm
outer radius – from 30 to 70 nm
thickness – 2 nm L R1 R2 z o
Cylindrical layer quantum dot

13. 2. Models of confining potentials1.
– Chakraborty-Pietilainen model
(Phys. Rev. B 50, 8460 (1994)). 2.
– Model of the impenetrable cylindrical layer quantum dot
(Physica E 36, 114 (2007) ) 3.
– Smorodinsky-Winternitz model
(Yadernaya fizika 4, 625 (1966)). 4.
– Radial analog of the Smorodinsky-Winternitz potential

14. 3. Quantum ring in the magnetic field

16. F(a,b,x) – confluent hypergeometrical function.
– effective mass of the electron ( – hole )
F(a,b,x) – confluent hypergeometrical function.

17. 4. Absorption coefficient

19. 5. Influence of electric fieldz o

21. 6. Rotator model L R1 R2 z o x

22. Rotational levels
Radial level

23. 7. Electronic states in the spherical nanolayer 1. E.M. Kazaryan, A.A. Kostanyan, H.A. Sarkisyan, J. Cont. Phys. (2007). 2. M.A. Zuhair, A.Kh. Manaselyan, H.A. Sarkisyan, J. Phys.: Conf. Ser. (2008).

25. Parabolic quantum well with hydrogen-like impurity
1A. A. Gusev, et al, Phys. At. Nucl., 2010, Vol. 73, (accepted).

28. THANK YOU!