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Considering hydrogen-like impurity and the thickness effect,the eigenvalues and eigenfunctions of the electron ground state and first exited state in a quantum dot (QD) are derived by using the Lee-Low-Pines-Pekar variational method with a parabolic confinement potential well (PCPW) and an asymmetric Gaussian functional confinement potential well (AGFCPW) serving as the transverse and longitudinal confinement potential,respectively.Based on the above two states,a two-level system is constructed.Then,the electron quantum transition affected by a magnetic field is discussed in terms of the two-level system theory.The numerical calculations indicate that the electron transition probability Q deceases with the range R0 of the PCPW decreasing.With R0 decreasing,the amplitude of the transition probability Q decreases greatly when R0 is small (R0 2.5rp),but the decrease becomes small when R0 is large (R0 2.5rp).The transition probability Q decreases with the dielectric constant ratio increasing.For different values of the well width L of the AGFCPW,the change forms of the transition probability Q with the well width L are different:the transition probability Q decreases monotonically with the decreasing of the well width L when L is large (L 1.3rp), which is similar to the trend of the transition probability Q changing with the range R0 of the PCPW,but the oscillation of the transition probability Q is small with the decreasing of the well width L when L is small (L 1.3rp).Whereas, both changes are consistent basically when the range of the confinement potential (the value of R0 or L) is large since the AGFCPW can be approximated by the PCPW when z/L ≪ 1.For the electronic state and its change in the QD with a confinement potential,in any case,the results are rough without regard to the influence arising from the thickness of the QD.This shows that the AGFCPW is more accurate than the PCPW in reflecting the real confinement potential. This conclusion is in accordance with the experimental results.In addition,the transition probability Q decreases with increasing V0.The amplitude of the transition probability Q decreasing with increasing the dielectric constant ratio is enlarged with reducing the coupling strength .This indicates that the phonon (the polarization of the medium) effect cannot be ignored when investigating the change of the electronic state in the QD.The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency c.The external magnetic field is a kind of inducement causing the quantum transition of electronic state.The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency c,and is affected dramatically by the coupling strength :with increasing the coupling strength ,the oscillation period of Q increases,but the oscillation amplitude decreases.In a word,the transition probability of the electron is influenced significantly by some physical quantities,such as the coupling strength ,the dielectric constant ratio ,the resonant frequency of the magnetic field c,the well depth V0, and the well width L of AGFCPW.
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Keywords:
- quantum dot /
- hydrogen-like impurity /
- asymmetric Gaussian functional confinement potential well /
- quantum transition
[1] Dou X M, Ying Y U, Sun B Q, Jiang D S, Ni H Q, Niu Z C 2012 Chin. Phys. Lett. 29 104203
[2] Wang H Y, Su D, Yang S, Dou X M, Zhu H J, Jiang D S, Ni H Q, Niu Z C, Zhao C L, Sun B Q 2015 Chin. Phys. Lett. 32 107804
[3] Yang S, Dou X M, Yu Y, Ni H Q, Niu Z C, Jiang D S, Sun B Q 2015 Chin. Phys. Lett. 32 077804
[4] Xue Y Z, Chen Z S, Ni H Q, Niu Z C, Jiang D S, Dou X M, Sun B Q 2017 Chin. Phys. B 26 084202
[5] Li B X, Zheng J, Chi F 2012 Chin. Phys. Lett. 29 107302
[6] Shi L, Yan Z W 2013 Eur. Phys. J. B 86 244
[7] Li B X, Zheng J, Chi F 2014 Chin. Phys. Lett. 31 057302
[8] Feng Z Y, Yan Z W 2016 Chin. Phys. B 25 107804
[9] Li W P, Xiao J L, Yin J W, Yu Y F, Wang Z W 2010 Chin. Phys. B 19 047102
[10] Chen Y J, Xiao J L 2013 J. Low Temp. Phys. 170 60
[11] Bai X F, Xin W, Yin H W, Eerdunchaolu 2017 Int. J. Theor. Phys. 56 1673
[12] Sun Y, Ding Z H, Xiao J L 2017 J. Electron. Mater. 46 439
[13] Gu J, Liang J J 2005 Acta Phys. Sin. 54 5335 (in Chinese)[谷娟, 梁九卿 2005 物理学报 54 5335]
[14] Fotue A J, Kenfack S C, Tiotsop M, Issofa N, Tabue Djemmo M P, Wirngo A V, Fotsin H, Fai L C 2016 Eur. Phys. J. Plus. 131 75
[15] Jacak L, Hawrylak P, Wojs A 1998 Quantum Dots (Berlin:Springer)
[16] Adamowski J, Sobkowicz M, Szafran B, Bednarek S 2000 Phys. Rev. B 62 4234
[17] Xie W F 2003 Solid State Commun. 127 401
[18] Hai G Q, Peeters F M, Devreese J T 1993 Phys. Rev. B 47 10358
[19] Liang S D, Chen C Y, Jiang S C, Lin D L 1996 Phys. Rev. B 53 15459
[20] Xiao J L 2016 Int. J. Theor. Phys. 55 147
[21] Khordad R, Goudarzi S, Bahramiyan H 2016 Indian J. Phys. 90 659
[22] Wei X W, Qi B, Xiao J L 2015 J. Low Temp. Phys. 179 166
[23] Miao X J, Sun Y, Xiao J L 2015 J. Korean Phys. Soc. 67 1197
[24] Lee T D, Low F M, Pines S D 1953 Phys. Rev. 90 297
[25] Landau L D, Pekar S I 1948 Zh. Eksp. Teor. Fiz. 18 419
[26] Pekar S I, Deigen M F 1948 Zh. Eksp. Teor. Fiz. 18 481
[27] Pekar S I 1954 Untersuchungen ber die Elektronentheorie der Kristalle (Berlin: Akademie Verlag)
[28] Li W P, Yin J W, Yu Y F, Xiao J L, Wang Z W 2009 Int. J. Theor. Phys. 48 3339
[29] Eerdunchaolu, Xiao J L 2007 J. Phys. Soc. Jpn. 76 044702
[30] Li S S, Kong X J 1992 J. Phys. Condens. Matter 4 4815
[31] Li S S, Xia J B 2007 J. Appl. Phys. 101 093716
[32] Li S S, Xia J B 2007 Phys. Lett. A 366 120
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[1] Dou X M, Ying Y U, Sun B Q, Jiang D S, Ni H Q, Niu Z C 2012 Chin. Phys. Lett. 29 104203
[2] Wang H Y, Su D, Yang S, Dou X M, Zhu H J, Jiang D S, Ni H Q, Niu Z C, Zhao C L, Sun B Q 2015 Chin. Phys. Lett. 32 107804
[3] Yang S, Dou X M, Yu Y, Ni H Q, Niu Z C, Jiang D S, Sun B Q 2015 Chin. Phys. Lett. 32 077804
[4] Xue Y Z, Chen Z S, Ni H Q, Niu Z C, Jiang D S, Dou X M, Sun B Q 2017 Chin. Phys. B 26 084202
[5] Li B X, Zheng J, Chi F 2012 Chin. Phys. Lett. 29 107302
[6] Shi L, Yan Z W 2013 Eur. Phys. J. B 86 244
[7] Li B X, Zheng J, Chi F 2014 Chin. Phys. Lett. 31 057302
[8] Feng Z Y, Yan Z W 2016 Chin. Phys. B 25 107804
[9] Li W P, Xiao J L, Yin J W, Yu Y F, Wang Z W 2010 Chin. Phys. B 19 047102
[10] Chen Y J, Xiao J L 2013 J. Low Temp. Phys. 170 60
[11] Bai X F, Xin W, Yin H W, Eerdunchaolu 2017 Int. J. Theor. Phys. 56 1673
[12] Sun Y, Ding Z H, Xiao J L 2017 J. Electron. Mater. 46 439
[13] Gu J, Liang J J 2005 Acta Phys. Sin. 54 5335 (in Chinese)[谷娟, 梁九卿 2005 物理学报 54 5335]
[14] Fotue A J, Kenfack S C, Tiotsop M, Issofa N, Tabue Djemmo M P, Wirngo A V, Fotsin H, Fai L C 2016 Eur. Phys. J. Plus. 131 75
[15] Jacak L, Hawrylak P, Wojs A 1998 Quantum Dots (Berlin:Springer)
[16] Adamowski J, Sobkowicz M, Szafran B, Bednarek S 2000 Phys. Rev. B 62 4234
[17] Xie W F 2003 Solid State Commun. 127 401
[18] Hai G Q, Peeters F M, Devreese J T 1993 Phys. Rev. B 47 10358
[19] Liang S D, Chen C Y, Jiang S C, Lin D L 1996 Phys. Rev. B 53 15459
[20] Xiao J L 2016 Int. J. Theor. Phys. 55 147
[21] Khordad R, Goudarzi S, Bahramiyan H 2016 Indian J. Phys. 90 659
[22] Wei X W, Qi B, Xiao J L 2015 J. Low Temp. Phys. 179 166
[23] Miao X J, Sun Y, Xiao J L 2015 J. Korean Phys. Soc. 67 1197
[24] Lee T D, Low F M, Pines S D 1953 Phys. Rev. 90 297
[25] Landau L D, Pekar S I 1948 Zh. Eksp. Teor. Fiz. 18 419
[26] Pekar S I, Deigen M F 1948 Zh. Eksp. Teor. Fiz. 18 481
[27] Pekar S I 1954 Untersuchungen ber die Elektronentheorie der Kristalle (Berlin: Akademie Verlag)
[28] Li W P, Yin J W, Yu Y F, Xiao J L, Wang Z W 2009 Int. J. Theor. Phys. 48 3339
[29] Eerdunchaolu, Xiao J L 2007 J. Phys. Soc. Jpn. 76 044702
[30] Li S S, Kong X J 1992 J. Phys. Condens. Matter 4 4815
[31] Li S S, Xia J B 2007 J. Appl. Phys. 101 093716
[32] Li S S, Xia J B 2007 Phys. Lett. A 366 120
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