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基于Lee-Low-Pines幺正变换，采用Pekar类型变分法研究了抛物量子点中强耦合磁双极化子的内部激发态性质，当考虑自旋和外磁场影响时，推导出二维量子点中强耦合磁双极化子基态的能量E0，声子平均数N0以及第一激发态的能量E1，声子平均数N1随量子点受限强度ω0，介电常数比η，电子-声子耦合强度α和磁场的回旋共振频率ωC的变化规律. 结果表明，磁双极化子的基态能量E0和第一激发态能量E1由两电子的单粒子能量EE，两电子间库仑相互作用能EC，电子自旋与磁场相互作用能Es和电子-声子相互作用能Ee-ph四部分组成；单粒子“轨道”运动与磁场相互作用导致了第一激发态能级E1分裂为E1（1+1），E1（1-1）两条，而电子自旋-磁场相互作用的效应又使基态和第一激发态的各能级均产生了三条“精细结构”；N0和N1随ω0，α和ωc的增加而增大，Ee-ph的取值总是小于零，其绝对值随α，ω0 和ωc的增加而增大；电子-声子相互作用的效应是束缚态磁双极化子形成的有力因素，而限定势和电子之间的库仑排斥能的存在不利于束缚态磁双极化子的形成；能量为E1（1-1）的磁双极化子要比能量为E1（1+1）的磁双极化子更容易且更稳定地处于束缚态.The properties of the internal excited state of the strong coupling magneto-bipolarons in a parabolic quantum dot are studied by using the variational method of Pekar type based on the Lee-Low-Pines’ unitary transformation. With the influences of the electronic spin and the external magnetic field taken into consideration, the change law of ground state energy E0, the average number of phonon N0, the first excited state energy E1 and the average number of phonon N1 of the magneto-bipolarons with the confinement strength ω0, the dielectric constant ratio η, the electron-phonon coupling α, and the cyclotron frequency ωc are derived in two-dimensional quantum dot. Numerical results indicate that the ground state energy E0 and the first excited state energy E1 consist of four parts: the single-article energy Ee of two electrons, the Coulomb interaction energy EC between two electrons, the interaction energy Es between the electronic spin and the external magnetic field, and the interaction energy Ee-ph of the electron with the longitudinalo optical phonons. The energy E1 of the first excited state splits into two lines, i.e., E1(1+1) and E1(1-1) due to the interaction between the “orbital” motion of the single-particle and the magnetic field, and each level of the ground-state energy and the first excited state energies set produces three “fine structures” due to the interaction between the electronic spin and the magnetic field. N0 and N1 increase with ω0, α and ωc increasing; Ee-ph is always less than zero, and absolute value |Ee-ph| increases with ω0, α and ωc increasing. The electron-phonon interaction has an important influence on the formation of bound state of the magneto-bipolaron; but the confinement potential and coulomb repulsive energy between electrons are unfavorable for the formation of magneto-bipolaron in the bound state.
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Keywords:
- quantum dot /
- magneto-bipolaron /
- internal excited state
[1] Li W S, Sun B Q 2013 Acta Phys. Sin. 62 047801 (in Chinese) [李文生, 孙宝权 2013 62 047801]
[2] Yang F, Zheng R S 2007 Solid State Commun. 141 555
[3] Zhu J, Ban S L, Ha S H 2012 Chin. Phys. B 21 097301
[4] Li Y, Zheng R S, Feng Y C, Liu S H, Niu H B 2006 Chin. Phys. B 15 702
[5] Shen M, Bai Y K, An X T, Liu J J 2013 Chin. Phys. B 22 047101
[6] Chen S H Yao Q Z 2011 Modern Phys. Lett. B 25 2419
[7] Kastner M A 1992 Rev. Mod. Phys. 64 849
[8] Loss D, Di Vincenzo D P 1998 Phys. Rev. A 57 120
[9] Burkard G, Loss D, Di Vincenzo D P 1999 Phys. Rev. B 59 2070
[10] Harju A, Siljamäki S, Nieminen R M 2002 Phys. Rev. Lett. 88 226804
[11] Chen Z S, Sun L L, Li S S 2004 J. Semicond. 25 790 (in Chinese) [陈早生, 孙连亮, 李树深 2004 半导体学报 25 790]
[12] Eerdunchaolu, Wuyunqimuge, Xiao X, Han C, Win W 2012 Commun. Theor. Phys. 57 157
[13] Emin D 1989 Phys. Rev. Lett. 62 1544
[14] Peng Q M, Sun J X, Li X J, Li M L, Li F 2011 Appl. Phys. Lett. 99 033509
[15] Schellekens A J, Wagemans W, Kersten S P, Bobbert P A, Koopmans B 2011 Phys. Rev. B 84 075204
[16] Pokatilov E P, Crotitoru M D, Fomin V M, Devreese J T 2003 Phys. Stat. Sol. B 237 244
[17] Senger R T, Ercelebi A R T 2002 J. Phys.: Condens Matt. 14 5549
[18] Ruan Y H, Chen Q H, Jiao Z K 2003 Int. J. Modern Phys. B 17 4332
[19] Hohenadler M, Littlewood P B 2007 Phys. Rev. B 76 155122
[20] Fai L C, Fomethe A, Fotue A J, Mborong V B, Domngang S, Issofa N, Tchoffo M 2008 Superlatt. Microstuct. 43 44
[21] Eerdunchaolu, Win W 2011 Physica B 406 358
[22] Xin W, Gao Z M, Wuyunqimuge, Han C, Eerdunchaolu 2012 Superlattice Microst. 52 872
[23] Lee T D, Low F M, Pines D 1953 Phys. Rev. 90 97
[24] Yildirim T, Ercelebi A 1999 J. Phys. Condens. Matter. 3 1271
[25] Schiff L 1986 Quantum Mechanics (3nd Ed) (New York: McGraw-Hill, Inc.) p375, p376
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[1] Li W S, Sun B Q 2013 Acta Phys. Sin. 62 047801 (in Chinese) [李文生, 孙宝权 2013 62 047801]
[2] Yang F, Zheng R S 2007 Solid State Commun. 141 555
[3] Zhu J, Ban S L, Ha S H 2012 Chin. Phys. B 21 097301
[4] Li Y, Zheng R S, Feng Y C, Liu S H, Niu H B 2006 Chin. Phys. B 15 702
[5] Shen M, Bai Y K, An X T, Liu J J 2013 Chin. Phys. B 22 047101
[6] Chen S H Yao Q Z 2011 Modern Phys. Lett. B 25 2419
[7] Kastner M A 1992 Rev. Mod. Phys. 64 849
[8] Loss D, Di Vincenzo D P 1998 Phys. Rev. A 57 120
[9] Burkard G, Loss D, Di Vincenzo D P 1999 Phys. Rev. B 59 2070
[10] Harju A, Siljamäki S, Nieminen R M 2002 Phys. Rev. Lett. 88 226804
[11] Chen Z S, Sun L L, Li S S 2004 J. Semicond. 25 790 (in Chinese) [陈早生, 孙连亮, 李树深 2004 半导体学报 25 790]
[12] Eerdunchaolu, Wuyunqimuge, Xiao X, Han C, Win W 2012 Commun. Theor. Phys. 57 157
[13] Emin D 1989 Phys. Rev. Lett. 62 1544
[14] Peng Q M, Sun J X, Li X J, Li M L, Li F 2011 Appl. Phys. Lett. 99 033509
[15] Schellekens A J, Wagemans W, Kersten S P, Bobbert P A, Koopmans B 2011 Phys. Rev. B 84 075204
[16] Pokatilov E P, Crotitoru M D, Fomin V M, Devreese J T 2003 Phys. Stat. Sol. B 237 244
[17] Senger R T, Ercelebi A R T 2002 J. Phys.: Condens Matt. 14 5549
[18] Ruan Y H, Chen Q H, Jiao Z K 2003 Int. J. Modern Phys. B 17 4332
[19] Hohenadler M, Littlewood P B 2007 Phys. Rev. B 76 155122
[20] Fai L C, Fomethe A, Fotue A J, Mborong V B, Domngang S, Issofa N, Tchoffo M 2008 Superlatt. Microstuct. 43 44
[21] Eerdunchaolu, Win W 2011 Physica B 406 358
[22] Xin W, Gao Z M, Wuyunqimuge, Han C, Eerdunchaolu 2012 Superlattice Microst. 52 872
[23] Lee T D, Low F M, Pines D 1953 Phys. Rev. 90 97
[24] Yildirim T, Ercelebi A 1999 J. Phys. Condens. Matter. 3 1271
[25] Schiff L 1986 Quantum Mechanics (3nd Ed) (New York: McGraw-Hill, Inc.) p375, p376
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