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

The idea of size-quantisation

Some geometries of quantum dots

Fulerens and nanotubes

Simple models of layered systems Z O R1 R2 X Y Z O Spherical layer QD Cylindrical layer QD

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.

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

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)).

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

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

2. Models of confining potentials 1. – 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

3. Quantum ring in the magnetic field

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

4. Absorption coefficient

5. Influence of electric field z o

6. Rotator model L R1 R2 z o x

Rotational levels Radial level

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).

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

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