量子点中双极化子和磁双极化子的研究进展
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摘要
综述了近年来对抛物线性限制势量子点中强耦合双极化子和磁双极化子的部分研究工作。从抛物量子点中2个电子-声子体系的哈密顿量出发,采用Lee-Low-Pines-Huybrechts变分方法,研究了量子点中强耦合双极化子的振动频率、诱生势和有效势随电子-声子耦合强度、两电子相对距离和量子点半径的变化规律;采用Tokuda改进的线性组合算符法研究了温度和LO声子效应对强耦合双极化子的有效质量和平均声子数的影响。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,研究了二维量子点中强耦合磁双极化子基态的能量、声子平均数以及第一激发态的能量、声子平均数随量子点受限强度、介电常数比、电子-声子耦合强度和磁场的回旋共振频率的变化规律。
This article is a review on our studies in recent years on the research progress of the bipolaron and the magneto-bipolaron in a parabolic quantum dot. Based on a Hamiltonian of the two electrons-longitudinal optical phonon system,the vibration frequency and the effective potential of the strong coupling bipolarons with the strength of the electron-phonon coupling and the relative distance between the electrons and the quantum dot's radius are derived using the Lee-Low-Pines-Huybrechts variational method. The influence of the temperature and the LO phonons on the average number of phonon and the effective mass of the strong-coupling bipolaron in a parabolic quantum dot have been investigated using the Tokuda modified linear-combination operator method. The properties of the internal excited state of the strong coupling magneto-bipolarons in a parabolic quantum dot are studied using the variation method of Pekar type based on the Lee-Low-Pines' unitary transformation. Considering the influence of the electronic spin and the external magnetic field,the ground state energy,the average number of phonon,the first excited state energy and the average number of phonon of the magneto-bipolarons with the confinement strength,the dielectric constant ratio,the electron-phonon coupling and the cyclotron frequency are derived in two-dimensional quantum dot.
This article is a review on our studies in recent years on the research progress of the bipolaron and the magneto-bipolaron in a parabolic quantum dot. Based on a Hamiltonian of the two electrons-longitudinal optical phonon system,the vibration frequency and the effective potential of the strong coupling bipolarons with the strength of the electron-phonon coupling and the relative distance between the electrons and the quantum dot's radius are derived using the Lee-Low-Pines-Huybrechts variational method. The influence of the temperature and the LO phonons on the average number of phonon and the effective mass of the strong-coupling bipolaron in a parabolic quantum dot have been investigated using the Tokuda modified linear-combination operator method. The properties of the internal excited state of the strong coupling magneto-bipolarons in a parabolic quantum dot are studied using the variation method of Pekar type based on the Lee-Low-Pines' unitary transformation. Considering the influence of the electronic spin and the external magnetic field,the ground state energy,the average number of phonon,the first excited state energy and the average number of phonon of the magneto-bipolarons with the confinement strength,the dielectric constant ratio,the electron-phonon coupling and the cyclotron frequency are derived in two-dimensional quantum dot.
引文
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[3]Li Z X,Xiao J L,Wang H Y.The effective mass of strong-coupled polaron in an asymmetric quantum dot induced with rashba effect[J].Modern Physics Letters B,2010,24(23):2 423-2 430.
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[10]Ruan Y H,Chen Q H,Jiao Z K.Variational Path-integral study on a bipolaron in a parabolic quantum wire or well[J].Internat J Modern Phys B,2003,17:4 332-4 337.
[11]Hohenadler M,Littlewood P B.Quantum Monte Carlo results for bipolaron stability in quantum dots[J].Phys Rev B,2007,76:155 122-155 126.
[12]Fai L C,Fomethe A,Fotue A J,et al.Bipolaron in a quasi-0D quantum dot[J].Superlatt Microstuct,2008,43:44-52.
[13]Eerdunchaolu,Wei Xin.Temperature dependence of the properties of strong-coupling bipolraon in a quantum dot[J].Physica B,2011,406:358-362.
[14]Xiao J L.Properties of a strong coupling bipolaron in an asymmetric quantum dot[J].J Low Temp Phys,2014,174:284-291.
[15]Huybrechts J.Note on the ground-state energy of the Feynman polaron[J].J Phys C:Solid State Phys,1976,9(8):211-212.
[16]Lee T D,Low F M,Pines D.The motion of slow electrons in a crystal[J].Phys Rev,1953,90(1):297-302.
[17]Xin W,Gao Z M,Wuyunqimuge,et al.Influence of temperature and LO phonon effects on the effective mass of quasi 0D bipolarons in the strong-coupling limit[J].Superlattices and Microstructures,2012,52:872-879.
[18]Tokuda N.A variational approach to the polaron problem[J].J Phys C:Solid State Phys,1980,13:L851-L855.
[19]Eerdunchaolu,Han C,Xin W,et al.Influence of magnetic field and lo phonon effects on the spin polarization state energy of strong-coupling bipolaron in a quantum dot[J].J Low Temp Phys,2014,174:301-310.
[20]Chatterjee A.Strong-coupling theory for the multidimensional free optical magnetopolaron[J].Phys Rev B,1990,41:1 668-1 670.
[21]Schiff L.Quantum Mechanics(3nded)[M].New York:McG raw-Hill,Inc,1968.
[2]Chen S H,Yao Q Z.The effective mass of strong-coupling magnetopolarons in a parabolic quantum dot[J].Modern Physics Letters B,2011,25(32):2 419-2 425.
[3]Li Z X,Xiao J L,Wang H Y.The effective mass of strong-coupled polaron in an asymmetric quantum dot induced with rashba effect[J].Modern Physics Letters B,2010,24(23):2 423-2 430.
[4]Xiao W,Xiao J L.The effective mass of strong-coupling magnetopolaron in quantum dot[J].Int J Mod Phys B,2007,21(12):2 007-2 016.
[5]Eerdunchaolu,Xin W,Zhao Y W.Influence of lattice vibration on the ground-state of magnetopolaron in a parabolic quantum dot[J].Modern Physics Letters B,2010,24(27):2 705-2 712.
[6]Adamowski J.Formation of a Frohlich bipolarons[J].Phys Rev B,1989,39:3 649-3 652.
[7]Pekar S I.Research on electron theory of crystals[M].Publisher:USABC,Washington D C,1963.
[8]Pokatilov E P,Crotitoru M D,Fomin V M,et al.Bipolaron stability in an ellipsoidal potential well[J].Phys Stat Sol(b),2003,237:244-251.
[9]Senger R T,Ercelebi A R T.On the stability of Frhlich bipolarons in spherical quantum dots[J].J Phys:Condens Matt,2002,14:5 549-5 560.
[10]Ruan Y H,Chen Q H,Jiao Z K.Variational Path-integral study on a bipolaron in a parabolic quantum wire or well[J].Internat J Modern Phys B,2003,17:4 332-4 337.
[11]Hohenadler M,Littlewood P B.Quantum Monte Carlo results for bipolaron stability in quantum dots[J].Phys Rev B,2007,76:155 122-155 126.
[12]Fai L C,Fomethe A,Fotue A J,et al.Bipolaron in a quasi-0D quantum dot[J].Superlatt Microstuct,2008,43:44-52.
[13]Eerdunchaolu,Wei Xin.Temperature dependence of the properties of strong-coupling bipolraon in a quantum dot[J].Physica B,2011,406:358-362.
[14]Xiao J L.Properties of a strong coupling bipolaron in an asymmetric quantum dot[J].J Low Temp Phys,2014,174:284-291.
[15]Huybrechts J.Note on the ground-state energy of the Feynman polaron[J].J Phys C:Solid State Phys,1976,9(8):211-212.
[16]Lee T D,Low F M,Pines D.The motion of slow electrons in a crystal[J].Phys Rev,1953,90(1):297-302.
[17]Xin W,Gao Z M,Wuyunqimuge,et al.Influence of temperature and LO phonon effects on the effective mass of quasi 0D bipolarons in the strong-coupling limit[J].Superlattices and Microstructures,2012,52:872-879.
[18]Tokuda N.A variational approach to the polaron problem[J].J Phys C:Solid State Phys,1980,13:L851-L855.
[19]Eerdunchaolu,Han C,Xin W,et al.Influence of magnetic field and lo phonon effects on the spin polarization state energy of strong-coupling bipolaron in a quantum dot[J].J Low Temp Phys,2014,174:301-310.
[20]Chatterjee A.Strong-coupling theory for the multidimensional free optical magnetopolaron[J].Phys Rev B,1990,41:1 668-1 670.
[21]Schiff L.Quantum Mechanics(3nded)[M].New York:McG raw-Hill,Inc,1968.