Investigation of Magnetic Field Effect onthe Quantum Dot with One Electron by Perturbation Method

Abstract

In this study we investigated the effect of an external magnetic field on the electronic properties of one-electron quantum dot using perturbation method. One electron quantum dot structure with hydrogen-like impurities at the center confined by finite parabolic potential was considered. Possible solutions of the Schrödinger equation of this structure were determined by the Quantum Genetic Algorithm (QGA), and energy eigenvaules of the quantum dot were calculated by Hartree-Fock- Roothaan Method (HFR). The wave functions of the system were constructed by linear combination of Slater Type Orbitals (STO). The contribution due to the paramagnetism and diamagnetism terms to the ground and some excited energies states of this structure were investigated depending on the radius of this structures.

Keywords

• Hartree-Fock Roothaan Method,Quantum Dot,Quantum Genetic Algorithm,Perturbation Method,Slater Type Orbital,Magnetic Field

Tek Elektronlu Kuantum Nokta Yapılarda Manyetik Alan Etkisinin Pertürbasyon Yöntemiyle İncelenmesi

Abstract

Bu çalışmada dış manyetik alan içinde tek elektronlu kuantum nokta yapının elektronik özellikleri pertürbasyon yöntemiyle incelendi. Sonlu derinlikli potansiyelle sınırlandırılmış merkezinde hidrojen benzeri safsızlık olan tek elektronlu kuantum nokta yapı ele alındı. Kuantum Genetik Algoritma (KGA) tekniği ile bu yapı için Schrödinger denkleminin olası çözümleri bulundu. Bu çözümler kullanılarak tek elektronlu kuantum nokta yapının enerjilerinin beklenen değerleri Hartree-Fock-Roothaan Metodu (HFR) kullanılarak hesaplandı. Sistemin dalga fonksiyonları Slater Tipi Orbitallerin (STO) lineer kombinasyonu şeklinde kuruldu. Bu nokta yapının taban ve bazı uyarılmış enerji seviyelerine paramanyetik ve diamanyetik terimden gelen katkılar kuantum nokta yarıçapına bağlı olarak incelendi.

Keywords

• Hartree-Fock-Roothaan Metot,Kuantum Nokta Yapı,Kuantum Genetik Algoritma,Pertürbasyon Yöntemi,Slater Tipi Orbital,Manyetik Alan

References

1. Anderson RL (1962). Experiments on Ge-GaAs heterojunctions. Solid-State Electron 5: 341-344.
2. Arfken G (1985). Mathematical Methods for Physics, Third Edition, Academic Press Inc, Orlando.
3. Castro CF, António CA, Sousa LC (2004). Optimisation of shape and process parameters in metal forging using genetic algorithms. Journal of Materials Processing Technology 146: 356-364.
4. Cho AY, Arthur JR (1975). Molecular beam epitaxy. Progress in Solid State Chemistry 10: 157-191.
5. Cibert J, Petroff PM, Dolan GJ, Pearton SJ, Gossard, AC, English JH (1986). Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes. Journal Applied Physics Letters 49: 1275-1277.
6. Cakir B, Ozmen A, Sahin M, Yakar Y, Atav U, Yüksel H (2006). Determination of wave functions of a quantum dot using the genetic algorithm. Proceedings of the international conference on modeling and simulation, Konya.
7. Çakır B (2007). Çok elektronlu kuantum nokta yapıların elektronik özelliklerinin incelenmesi, Selçuk Üniversitesi Fen Bilimleri Enstitüsü, Konya.
8. Cakir B, Ozmen A, Atav U, Yüksel H, Yakar Y (2007). Investigation of electronic structure of a quantum dot using slater-type orbitals and quantum genetic algorithm. International Journal Of Modern Physics C 18: 61-72.

9. Cakir B, Ozmen A, Atav U, Yüksel H, ve Yakar Y (2008). Calculation of electronic structure of a spherical quantum dot using a combination of quantum genetic algorithm and Hartree-Fock-Roothaan method. International Journal of Modern Physics C 19(4): 599-609.
10. Cakir B, Yakar Y, Ozmen A, (2012). Refractive index changes and absorption coefficients in a spherical quantum dot with parabolic potential. Journal of Luminescence 132: 26-59.
11. Cakir B, Yakar Y, Ozmen A (2013). Calculation of oscillator strength and the effects of electric field on energy states, static and dynamic polarizabilities of the confined hydrogen atom. Optics Communications 311: 222–228.
12. Cakir B, Yakar Y, Ozmen A (2015). Linear and nonlinear optical absorption coefficients of two-electron spherical quantum dot with parabolic potential. Physica B 458: 138–143.
13. Dineykhan M, Nazmitdinov RG (1997). Two-electron quantum dot in a magnetic field: analytical results. Phyical Review B 55: 13707-13714.
14. Fal’ko VI, Efetov KB (1994). Statistics of fluctuations of wave functions of chaotic electrons in a quantum dot in an arbitrary magnetic field. Physical Review B 50(15): 11267-11270.
15. Hall RN, Fenner GE, Kingsley JD, Soltys TJ (1962). Coherent light elemission from GaAs junctions. Physical Review Letters 9: 366-368.
16. Halonen V, Chakraborty T, Pietiläinen P (1992). Excitons in a parabolic quantum dot in magnetic fields. Physical Review B 45(11): 5980-5985.
17. Homaifar A, Lai HY, Cormick E (1994). System optimization of turbofan engines using genetic algorithms. Applied Mathematical Modelling 18: 72-83.
18. Kulkarni AJ, Krishnamurthy K, Deshmukh SP (2004). Microstructural optimization of alloys using a genetic algorithm. Materials Science and Engineering A 372: 213-220.
19. Nomura S, Segawa Y, Kobayashi T (1994). Confined excitons in a semiconductor quantum dot in a magnetic field. Physical Review B 49(19): 13571-13582.
20. Oaknin JH, Palacios JJ, Brey L, Tejedor C (1994). Self-consistent Hartree description of N electrons in a quantum dot with a magnetic field. Physical Review B 49(8): 5718-5721.
21. Schrieffer JR (1957). In Semiconductor surface physics. University of Pennsylvania Press, Philadelphia.
22. Sharkey J, Yoo C, Peter AJ (2010). Magnetic field induced diamagnetic susceptibility of a hydrogenic donor in a GaN/AlGaN quantum dot. Superlattices and Microstructures 48(2): 248-255.
23. Shunji A, Masami C, Tachishige H, Shojiro N, Yuki N, Toshiyuki S (1994). Precise measurements of e+e− annihilation at rest into four photons and the search for exotic particles. Physical Review A: 3201.
24. Sahin O, Sayan P, Bulutcu AN (2000). Application of genetic algorithm for determination of mass transfer coefficients. Journal of Crystal Growth 216: 475-482.
25. Temkin H, Dolan GJ, Panish MB, Chu SN (1987). Low-temperature photoluminescence from InGaAs/InP quantum wires and boxes. Applied Physics Letters 50: 413-415.
26. Venugopal V, Narendran TT (1992). A genetic algorithm approach to the machine-component grouping problem with multiple objectives. Computers & Industrial Engineering 22: 469-480.
27. Wojs A, Hawrylak P (1996). Charging and infrared spectroscopy of self-assembled quantum dots in a magnetic field. Physical Review B 53: 10841-10845.
28. Yakar Y, Ozmen A, Cakir B, Yüksel H (2007). Computation of rotation matrices making lined-up to the local Cartesian coordinates. Journal of the Chinese Chemical Society 54(5): 1139-1144.
29. Yakar Y, Cakir B, Ozmen A, (2010a). Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential. Optics Communications 283: 1795-1800.
30. Yakar Y, Cakir B, Ozmen A (2010b). Linear and nonlinear optical properties in spherical quantum dots. Communications in Theoretical Physics 53: 1185–1189.
31. Yakar Y, Cakir B, Ozmen A (2011). Computation of ionization and various excited state energies of helium and helium-like quantum dots. International Journal of Quantum Chemistry 111: 4139-4149.
32. Yakar Y, Cakir B, Ozmen A, (2013a). Computation of relativistic terms in a spherical quantum dot. Journal of Luminescence 134: 778-783.
33. Yakar Y, Cakir B, Ozmen A (2013b). Off-center hydrogenic impurity in spherical quantum dot with parabolic potential. Superlattices and Microstructures 60: 389-397.
34. Yakar Y, Cakir B, Ozmen A (2015a) Linear and nonlinear absorption coefficients of spherical two-electron quantum dot. Computer Physics Communications 188: 88–93.
35. Yakar Y, Cakir B, Ozmen A (2015b). Electronic structure of two-electron quantum dot with parabolic potential. Philosophical Magazine 95: 311–325.