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The influence of Rashba effect and Zeeman effect on the properties of bound magnetopolaron in an anisotropic quantum dot are studied with Pekar variational method. The expression of the ground state energy of the bound magnetopolaron is obtained through theoretical derivation. The relationship of the ground state energy of the polaron with the transverse effective confinement length, the longitudinal effective confinement length, the magnetic field cyclotron resonance frequency, and the Coulomb bound potential are discussed, respectively. Owing to the crystal structural inversion asymmetry and the time inversion asymmetry, the polaron energy experiences Rashba spin-orbit splitting and Zeeman splitting. Under the strong and weak magnetic field, we discuss the dominant position of Zeeman effect and Rashba effect, respectively. Owing to the presence of phonons and impurities, the polaron is more stable than the bare electron state.
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Keywords:
- Rashba effect /
- Zeeman effect /
- bound magnetopolaron /
- anisotropic quantum dot
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图 1 取固定值ωc = 1ωLO, l2 = 1.2, α = 8, αR = 1, 当库仑束缚势β' 取不同值时, 束缚磁极化子基态能量E与横向有效受限长度l1之间的关系曲线
Figure 1. For fixedωc = 1ωLO, l2 = 1.2, α = 8, αR = 1, the relation of bound magnetopoloran ground state enegergy E with the transverse effectiveconfinement length l1 at different Coulomb bound potential β'.
图 2 取固定值ωc = 1ωLO, l1 = 0.6, α = 8, αR = 1, 当库仑束缚势β' 取不同值时, 束缚磁极化子基态能量E与纵向有效受限长度l2之间的关系曲线
Figure 2. For fixedωc = 1ωLO, l1 = 0.6, α = 8, αR = 1, the relation of bound magnetopoloran ground state enegergy E with the longitudinal effectiveconfinement length l2 at different Coulomb bound potential β'.
图 3 取固定值ωc = 10ωLO, l2 = 1.2, α = 8, αR = 1, 当库仑束缚势β'取不同值时, 束缚磁极化子基态能量E与横向有效受限长度l1之间的关系曲线
Figure 3. For fixedωc = 10ωLO, l2 = 1.2, α = 8, αR = 1, the relation of bound magnetopoloran ground state enegergy E with the transverse effective confinement length l1 at different Coulomb bound potential β'.
图 4 取固定值ωc = 10ωLO, l1 = 0.6, α = 8, αR = 1, 当库仑束缚势β' 取不同值时, 束缚磁极化子基态能量E与纵向有效受限长度l2之间的关系曲线
Figure 4. For fixedωc = 10ωLO, l1 = 0.6, α = 8, αR = 1, the relation of bound magnetopoloran ground state enegergy E with the longitudinal effectiveconfinement length l2 at different Coulomb bound potential β'.
图 5 取固定值l1 = 0.4, l2 = 0.8, α = 8, αR = 0.5, 当库仑束缚势β' 取不同值时, 束缚磁极化子基态能量E与磁场回旋共振评率ωc之间的关系曲线
Figure 5. For fixed l1 = 0.4, l2 = 0.8, α = 8, αR = 0.5, the relation of bound magnetopoloran ground state enegergy E with the magnetic field resonance cyclotron frequency ωc at different Coulomb bound potential β'.
图 6 Rashba参量αR取不同值时, 自旋-轨道分裂能ESO与磁场回旋共振频率ωc之间的关系曲线
Figure 6. Change of spin-orbit splitting energy ESO with the magnetic field resonance cyclotron frequencyωcat different Rashba parameter αR.
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[1] Rashba E I, Efros A L 2003 Phys. Rev. Let. 91 126405
Google Scholar
[2] Chi F, Liu L, Sun L 2017 Chin. Phys. B 26 037304
Google Scholar
[3] Liu J, Xiao J L, Huo S F, Chen Z Y 2007 Commun. Theor. Phys. 48 930
Google Scholar
[4] Shan S P, Chen S H, Hu C, Zhuang R Z 2019 Int. J. Theor. Phys. 58 3702
Google Scholar
[5] 施婷 婷, 汪六九, 王璟琨, 张威 2020 69 016701
Google Scholar
Shi T T, Wang L J, Wang J K, Zhang W 2020 Acta Phys. Sin. 69 016701
Google Scholar
[6] Chen Y J, Cui C F, Liu W F, Shao F L 2020 Int. J. Theor. Phys. 6 1829
[7] Zamani A, Setareh F, Azargoshasb T, et al. 2017 Sperlattice Microst. 106 111
[8] Zhang H R, Xiao J L 2010 Chin. J. Lumi. 31 12
[9] Data S, Das B 1990 Appl. Phys. Lett. 56 665
Google Scholar
[10] Chi F, Liu L M 2018 Int. J. Theor. Phys. 57 562
Google Scholar
[11] Chi F, Sun L L 2016 Chin. Phys. Lett. 33 117201
Google Scholar
[12] Hofmann A, Maisi V F, Krähenmann T, et al. 2017 Phys. Rev. Lett. 119 176807
Google Scholar
[13] Ferdous R, Chan K W, Veldhorst M, et al. 2018 Phys. Rev. B 97 241401
Google Scholar
[14] Governale M 2002 Phys. Rev. Lett. 892 06802
[15] Li W P, Yin J W, Yu Y F, Xiao J L 2010 J. Low Temp. Phys. 160 112
[16] Yin J W, Li W P, Yu Y F, Xiao J L 2011 J. Low Temp. Phys. 163 53
[17] Lee J, Spector H N 2006 J. Appl. Phys. 99 113708
Google Scholar
[18] Bandyopadhyay S, Cahay M 2002 Superlattice Microst. 32 171
Google Scholar
[19] Li Z X, Yin C H, Zhu X Y 2015 Mode. Phys. Lett. B 29 1550124
[20] Peeters F M, Wu X G, Devreese J T 1986 Phys. Rev. B 33 3926
Google Scholar
[21] Shan S P, Chen S H, Xiao J L 2014 Low Temp. Phys. 40 712
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