THE SPIN-ORBIT INTERACTIONS OF ELECTRONS IN QUANTUM DOT
30 16
Abstract
The alternative method is suggested for taking into account the influence of each layer to explain the mechanism of blocking electrons in a quantum dot . The inclusion of the multilayer structure of nanocrystal leads to additional interactions between electrons in quantum dot and this potential is analytically derived. When the relation of distance of electrons is sufficiently small, the additional potential becomes parabolic. The dependence of frequency of the parabolic potential on the difference of dielectric permeability of layers is determined. We assume that the spin-orbital interactions of electrons in quantum dot are defined in an analogous way as a quarks in the nonrelativistic potential model of hadrons. Starting from this suggestion the spin-orbital interactions of electrons in quantum dot are defined. The dependence of the coupling constant of spin-orbital interactions on the image charge and effective size of quantum dot is studied.
References
1. T. Chakraborty, Comm. Cond. Matt. Phys. 16, 35 (1992); M.A. Kastner, Phys. Today. 46, 24 (1993); L. Jacak, P. Hawrylak, A. Wojs, Quantum Dots. - Berlin: Springer Verlag, (1997).
2. R. Turton, The Quantum Dot, A Journey into Future Microelectronics. - New York: Ox-ford University Press, (1995).
3. R.C. Ashoori, H.L. Stormer, J.S. Weiner, et al., Phys. Rev. Lett. 71, 613 (1993); R.C.Ashoori, Nature (London), 379, 413 (1996).
4. M. Maksym, T. Chakraborty, Phys. Rev. Lett. 65, 108 (1990); Phys. Rev. B 45, 1947 (1992); U. Merkt, J. Huser, M. Wagner, Phys. Rev. B 43, 7320 (1991); M. Wagner, U. Merkt, A.V. Chaplik, Phys. Rev. B 45, 1951 (1992); M. Dineykhan, R.G. Nazmitdinov, Phys. Rev. B 55, 13707 (1997); J. Phys.: Cond. Matt. 11, 83 (1999).
5. S.A. Wolf, D.D. Awschalom, R.A. Buhzman, J.M. Daughton, S.von. Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.V. Trager, Science 294, 1488 (2001).
6. G. Dresselhaus, Phys.Rev. 100, 580 (1955); E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2, 1224 (1960)[Sov. Phys. Solid State 2, 1109 (1960)]; Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984); E.I. Rashba, Phys. Rev. B 62, 16267 (2000).
7. M. Dineykhan, G.V. Efimov, Sov Jour.Part.Nucl. 26, 651 (1995); M. Dineykhan, G.V. Efi-mov, G. Ganbold and S.N. Nedelko, Oscillator representation in quantum physics Lecture Notes in Physics, m 26. - Berlin: Springer Verlag, (1995).
8. L.D. Landau and E.M.Lifschitz, Electrodynamics of continuous media, Pergamon, Ox-ford (1987).
9. N.A. Gippius, V.D. Kulakovskii, S.G Tikhodeev, Usphehi Phys. Nauk 167, 558 (1997).
10. E.A. Mulyarov, S.G Tikhodeev, Jour. Exper. Theor. Phys., 84, 151 (1997).
11. M. Dineykhan, S.A. Zhaugasheva and R.G. Nazmitdinov, Jour. Exper. Theor. Phys., 92,1049 (2001).
12. M.Born, R. Oppenheimer, Ann. d.phys., Bd84, 457(1927). [13] M.Born, V.Fock, Zs.phys., Bd51, 165 (1928).
13. M.Born, V.Fock, Zs.phys., Bd51, 165 (1928).
14. I.V.Komarov, L.I.Ponomarev, and S.Yu. Slavyanov, Spheroidal and Coulomb Spheroidal Functions (Nauka, Moscow, 1976); S.I.Vinitski, and L.I.Ponomarev, Sov Jour.Part.Nucl., 13, 557 (1982).
15. M. Abramowitz and I.A.Stegun, Handbook of mathematical functions with formulas graphs and mathematical tables, National bureau of Standorts Applied Mathematics. Series ,(1964).
16. E. A. Solov'ev, Usphehi Phys. Nauk, 157, 437(1989); G.Jaffe, Z.Phys., 87, 535(1934); W.G.Beber and H.R.Hasse, Proc.Cambr.Philos. Soc.,31, 564(1935); D.R.Bates, K.Ledsham, and A.L.Stewart, Philos, Trans. R.Sos. London, Ser. A 246, 215 (1953).
17. V.A. Fock, The Principles of Quantum Mechanics(Nauka, Moscow, 1976; Mir,Moscow, 1978).
18. V.A.Fok, Izv. Akad. Nauk SSSR, Ser.Fiz. 18, 161 (1954).
19. M.Dineykhan, S.Zhaugasheva, O.Imambekov and Sh.Sarsembinov. Analitical determina-tion spin-orbit interactions and mechanism blocking electrons in quantum dot. (In press.)
20. W. Lucha, F. Schoberl, D. Gromes, Phys. Reports. 200, 127 (1991).
21. V.V. Golubkov, A.I. Ekimov, A.A. Onushenko, Phys. Chim. glass (in russian) 6, 511 (1980); .G. Bawendi et al., Phys. Rev. Lett. 65, 1623 (1990); A.I. Ekimov, Al.L. Efros, A.A. Onushenko, Sol. St. Comm. 88, 947 (1993).
22. V.V. Poborchii, M.S. Ivanova, I.A. Salamatina, Superlattices and Microstructures 16, 133 (1944); V. Dneprovskii, N. Gushina, E. Zhukov, Phys. Lett. A 204, 59 (1995).
23. L.T. Canham, Appl. Phus. Lett. 57, 1046 (1990).
24. A.A. Shashkin, Usphehi Phys. Nauk, 175, 129 (2005); Ph.L. Orlov, N.A. Ibina, Fiz. Tverd. Tela, 46, 913 (2004).
25. G. Lucovsky, R.M. White, et al., Sol. St. Comm., 18, 811 (1976).
26. G. Engels, J. Lange, Th. Shapers and H. Luth, Phys. Rev. B 55, 1958 (1997). Th. Schap-ers, G. Engels, J. Lange, Th. Klocke, M. Hollfelder and H. Luth, J. Appl. Phys., 83, 4324 (1998).
2. R. Turton, The Quantum Dot, A Journey into Future Microelectronics. - New York: Ox-ford University Press, (1995).
3. R.C. Ashoori, H.L. Stormer, J.S. Weiner, et al., Phys. Rev. Lett. 71, 613 (1993); R.C.Ashoori, Nature (London), 379, 413 (1996).
4. M. Maksym, T. Chakraborty, Phys. Rev. Lett. 65, 108 (1990); Phys. Rev. B 45, 1947 (1992); U. Merkt, J. Huser, M. Wagner, Phys. Rev. B 43, 7320 (1991); M. Wagner, U. Merkt, A.V. Chaplik, Phys. Rev. B 45, 1951 (1992); M. Dineykhan, R.G. Nazmitdinov, Phys. Rev. B 55, 13707 (1997); J. Phys.: Cond. Matt. 11, 83 (1999).
5. S.A. Wolf, D.D. Awschalom, R.A. Buhzman, J.M. Daughton, S.von. Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.V. Trager, Science 294, 1488 (2001).
6. G. Dresselhaus, Phys.Rev. 100, 580 (1955); E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2, 1224 (1960)[Sov. Phys. Solid State 2, 1109 (1960)]; Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984); E.I. Rashba, Phys. Rev. B 62, 16267 (2000).
7. M. Dineykhan, G.V. Efimov, Sov Jour.Part.Nucl. 26, 651 (1995); M. Dineykhan, G.V. Efi-mov, G. Ganbold and S.N. Nedelko, Oscillator representation in quantum physics Lecture Notes in Physics, m 26. - Berlin: Springer Verlag, (1995).
8. L.D. Landau and E.M.Lifschitz, Electrodynamics of continuous media, Pergamon, Ox-ford (1987).
9. N.A. Gippius, V.D. Kulakovskii, S.G Tikhodeev, Usphehi Phys. Nauk 167, 558 (1997).
10. E.A. Mulyarov, S.G Tikhodeev, Jour. Exper. Theor. Phys., 84, 151 (1997).
11. M. Dineykhan, S.A. Zhaugasheva and R.G. Nazmitdinov, Jour. Exper. Theor. Phys., 92,1049 (2001).
12. M.Born, R. Oppenheimer, Ann. d.phys., Bd84, 457(1927). [13] M.Born, V.Fock, Zs.phys., Bd51, 165 (1928).
13. M.Born, V.Fock, Zs.phys., Bd51, 165 (1928).
14. I.V.Komarov, L.I.Ponomarev, and S.Yu. Slavyanov, Spheroidal and Coulomb Spheroidal Functions (Nauka, Moscow, 1976); S.I.Vinitski, and L.I.Ponomarev, Sov Jour.Part.Nucl., 13, 557 (1982).
15. M. Abramowitz and I.A.Stegun, Handbook of mathematical functions with formulas graphs and mathematical tables, National bureau of Standorts Applied Mathematics. Series ,(1964).
16. E. A. Solov'ev, Usphehi Phys. Nauk, 157, 437(1989); G.Jaffe, Z.Phys., 87, 535(1934); W.G.Beber and H.R.Hasse, Proc.Cambr.Philos. Soc.,31, 564(1935); D.R.Bates, K.Ledsham, and A.L.Stewart, Philos, Trans. R.Sos. London, Ser. A 246, 215 (1953).
17. V.A. Fock, The Principles of Quantum Mechanics(Nauka, Moscow, 1976; Mir,Moscow, 1978).
18. V.A.Fok, Izv. Akad. Nauk SSSR, Ser.Fiz. 18, 161 (1954).
19. M.Dineykhan, S.Zhaugasheva, O.Imambekov and Sh.Sarsembinov. Analitical determina-tion spin-orbit interactions and mechanism blocking electrons in quantum dot. (In press.)
20. W. Lucha, F. Schoberl, D. Gromes, Phys. Reports. 200, 127 (1991).
21. V.V. Golubkov, A.I. Ekimov, A.A. Onushenko, Phys. Chim. glass (in russian) 6, 511 (1980); .G. Bawendi et al., Phys. Rev. Lett. 65, 1623 (1990); A.I. Ekimov, Al.L. Efros, A.A. Onushenko, Sol. St. Comm. 88, 947 (1993).
22. V.V. Poborchii, M.S. Ivanova, I.A. Salamatina, Superlattices and Microstructures 16, 133 (1944); V. Dneprovskii, N. Gushina, E. Zhukov, Phys. Lett. A 204, 59 (1995).
23. L.T. Canham, Appl. Phus. Lett. 57, 1046 (1990).
24. A.A. Shashkin, Usphehi Phys. Nauk, 175, 129 (2005); Ph.L. Orlov, N.A. Ibina, Fiz. Tverd. Tela, 46, 913 (2004).
25. G. Lucovsky, R.M. White, et al., Sol. St. Comm., 18, 811 (1976).
26. G. Engels, J. Lange, Th. Shapers and H. Luth, Phys. Rev. B 55, 1958 (1997). Th. Schap-ers, G. Engels, J. Lange, Th. Klocke, M. Hollfelder and H. Luth, J. Appl. Phys., 83, 4324 (1998).
Downloads
Published
2008-10-26
Issue
Section
Theoretical Physics. Nuclear and Elementary Particle Physics. Astrophysics
