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In this paper, based on the Lee-Low-Pines transformation, the ground-state properties of the bipolaron with the Rashba spin-orbit coupling effect in the quantum dot are studied by using the Pekar variational method. The expressions for the ground-state interaction energy Eint and binding energy Eb of the bipolaron are derived. The results show that Eint is composed of four parts: the electron-longitudinal optical (LO) phonon coupling energy Ee-ph, confinement potential of the quantum dot Ecouf, Coulomb energy between two electrons Ecoul and additional term in the Rashba spin splitting energy ER-ph originating from the LO phonon, where Ecouf and Ecoul are positive definite. These indicate that Ecouf and Ecoul are the repulsive potential of the bipolaron. Generally, it is unable to form the electron-electron coupling structure in the quantum dot because two electrons repel each other by means of the screened Coulomb potential and confinement potential of the quantum dot. However, the numerical results show that the ground-state binding energy of the bipolaron Eb is greater than zero under the condition of the electron-phonon strong coupling (coupling strength 6), so the condition of forming the steady bipolaron structure in quantum dots is naturally met (binding energy Eb 0). In addition, the ground-state energy of the bipolaron E is always less than zero, thus the ground-state biplaron in the quantum dot is in the steady bound state. This can be explained by the physical mechanism. Firstly, the electron-LO phonon coupling energy Ee-ph in the ground-state interaction energy of the bipolaron is always negative. Secondly, the electron-LO phonon coupling interaction in the low-dimensional structures of II-VI semiconductors is great enough (generally 6.0) so that the electron-LO phonon coupling energy Ee-ph is dominant in the ground-state energy E and, therefore the screened Coulomb potential and confinement potential of the quantum dot can be overcome and a steady electron-electron structure can be formed. The numerical results also indicate that the binding energy of the bipolaron Eb increases with increasing the confinement strength of quantum dot 0, dielectric constant ratio of medium and electronphonon coupling strength , but it shows the direct opposite cases from linear increase to decrease with increasing the Rashba spin-obit coupling strength R; the ground-state energy of the bipolaron splits into three energy levels due to the Rashba effect: E(), E() and E(), which correspond to spin orientations of two electrons respectively: up, down and antiparallel; the absolute value of ground-state energy |E| increases with increasing and , but it shows the direct opposite cases from linear increase to decrease with increasing the Rashba spin-obit coupling strength R; the electron-phonon coupling energy obviously accounts for a larger proportion than that of the Rashba spin-obit coupling energy in the ground-state energy of the bipolaron, but the electron-phonon coupling and Rashba spin-obit coupling infiltrate each other and influence each other significantly. In short, the electron in narrow-gap II-VI heterojunctions have higher Rashba spin splitting energy and larger application range. For these quantum dot structures, it is impossible and unnecessary to inhibit the formation of bipolarons. It is more accurate that the bipolaron is chosen as the elementary excitation than the single polaron when investigating the electron-phonon interaction and Rashba spin-orbit coupling, and the bipolaron has more practical significances and potential application values.
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Keywords:
- narrow-gap II-VI heterojunction /
- bipolaron /
- Rashba spin-obit coupling /
- ground-state energy
[1] Rashba E I, Tela F T 1960 Sov. Phys. Solid State 2 1109
[2] Bychkov Y A, Rashba E I 1984 J. Phys. C 17 6039
[3] Das B, Datta S, Reifenberger R 1990 Phys. Rev. B 41 8278
[4] Datta S, Das B 1990 Appl. Phys. Lett. 56 665
[5] Nitta J, Akazaki T, Takayanagi H, Enoki T 1997 Phy. Rev. Lett. 78 1335
[6] Engels G, Lange J, Schapers T, Lth H 1997 Phys. Rev. B 55 R1958
[7] Hu C M, Nitta J, Akazaki T, Takayanagi H, Osaka J, Pfeffer P, Zawadzki W 1999 Phys. Rev. B 60 7736
[8] Winkler R 2000 Phys. Rev. B 62 4245
[9] Rossler U, Malcher F, Lommer G 1989 High Magnetic Fields in Semiconductor Physics II (Berlin: Springer-Verlag) p376
[10] Zhang X C, Pfeufer-Jeschke A, Ortner K, Hock V, Buhmann H, Becker C R, Landwehr G 2001 Phys. Rev. B 63 245305
[11] Qiu Z J, Gui Y S, Shu X Z, Dai N, Guo S L, Chu J H 2004 Acta Phys. Sin. 53 1186 (in Chinese) [仇志军, 桂永胜, 疏小舟, 戴宁, 郭少令, 褚君浩 2004 53 1186]
[12] Tsitsishvili E, Lozano G S, Gogolin A O 2004 Phys. Rev. B 70 115316
[13] Manvir S, Kushwaha 2008 J. Appl. Phys. 104 083714
[14] Li J L, Li Y X 2010 Chin. Phys. Lett. 27 057202
[15] Hassanabadi H, Rahimov H, Zarrinkamar S 2012 Few-body Syst. 52 87
[16] Yin J W, Li W P, Yu Y F, Xiao J L 2011 J. Low Temp. Phys. 163 53
[17] Shan S P, Chen S H, Xiao J L 2014 J. Low Temp. Phys. 176 93
[18] Fai L C, Teboul V, Monteil A, Maabou A, Nsangou I 2005 Condens. Matter Phys. 8 639
[19] Pan J S 1985 Phys. Status. Solid B 127 307
[20] Zhao Y W, Han C, Xin W, Eerdunchaolu 2014 Superlattices Microstruct. 74 198
[21] Eerdunchaolu, Bai X F, Han Chao 2014 Acta Phys. Sin. 63 027501 (in Chinese) [额尔敦朝鲁, 白旭芳, 韩超 2014 63 027501]
[22] Lommer G, Malcher F, Rossler U 1988 Phys. Rev. Lett. 60 728
[23] Sun Q F, Wang J, Guo H 2005 Phys. Rev. B 71 165310
[24] Voskoboynikov O, Lee C P, Tretyak O 2001 Phys. Rev. B 63 165306
[25] Lee T D, Low F M, Pines D 1953 Phys. Rev. 90 297
[26] Yildirim T, Ercelebi A 1999 J. Phys. Conden. Matt. 3 1271
[27] Adamowski J 1989 Phys. Rev. B 39 3649
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[1] Rashba E I, Tela F T 1960 Sov. Phys. Solid State 2 1109
[2] Bychkov Y A, Rashba E I 1984 J. Phys. C 17 6039
[3] Das B, Datta S, Reifenberger R 1990 Phys. Rev. B 41 8278
[4] Datta S, Das B 1990 Appl. Phys. Lett. 56 665
[5] Nitta J, Akazaki T, Takayanagi H, Enoki T 1997 Phy. Rev. Lett. 78 1335
[6] Engels G, Lange J, Schapers T, Lth H 1997 Phys. Rev. B 55 R1958
[7] Hu C M, Nitta J, Akazaki T, Takayanagi H, Osaka J, Pfeffer P, Zawadzki W 1999 Phys. Rev. B 60 7736
[8] Winkler R 2000 Phys. Rev. B 62 4245
[9] Rossler U, Malcher F, Lommer G 1989 High Magnetic Fields in Semiconductor Physics II (Berlin: Springer-Verlag) p376
[10] Zhang X C, Pfeufer-Jeschke A, Ortner K, Hock V, Buhmann H, Becker C R, Landwehr G 2001 Phys. Rev. B 63 245305
[11] Qiu Z J, Gui Y S, Shu X Z, Dai N, Guo S L, Chu J H 2004 Acta Phys. Sin. 53 1186 (in Chinese) [仇志军, 桂永胜, 疏小舟, 戴宁, 郭少令, 褚君浩 2004 53 1186]
[12] Tsitsishvili E, Lozano G S, Gogolin A O 2004 Phys. Rev. B 70 115316
[13] Manvir S, Kushwaha 2008 J. Appl. Phys. 104 083714
[14] Li J L, Li Y X 2010 Chin. Phys. Lett. 27 057202
[15] Hassanabadi H, Rahimov H, Zarrinkamar S 2012 Few-body Syst. 52 87
[16] Yin J W, Li W P, Yu Y F, Xiao J L 2011 J. Low Temp. Phys. 163 53
[17] Shan S P, Chen S H, Xiao J L 2014 J. Low Temp. Phys. 176 93
[18] Fai L C, Teboul V, Monteil A, Maabou A, Nsangou I 2005 Condens. Matter Phys. 8 639
[19] Pan J S 1985 Phys. Status. Solid B 127 307
[20] Zhao Y W, Han C, Xin W, Eerdunchaolu 2014 Superlattices Microstruct. 74 198
[21] Eerdunchaolu, Bai X F, Han Chao 2014 Acta Phys. Sin. 63 027501 (in Chinese) [额尔敦朝鲁, 白旭芳, 韩超 2014 63 027501]
[22] Lommer G, Malcher F, Rossler U 1988 Phys. Rev. Lett. 60 728
[23] Sun Q F, Wang J, Guo H 2005 Phys. Rev. B 71 165310
[24] Voskoboynikov O, Lee C P, Tretyak O 2001 Phys. Rev. B 63 165306
[25] Lee T D, Low F M, Pines D 1953 Phys. Rev. 90 297
[26] Yildirim T, Ercelebi A 1999 J. Phys. Conden. Matt. 3 1271
[27] Adamowski J 1989 Phys. Rev. B 39 3649
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