Journal of Low Temperature Physics

, Volume 174, Issue 5–6, pp 301–310 | Cite as

Influence of Magnetic Field and LO Phonon Effects on the Spin Polarization State Energy of Strong-Coupling Bipolaron in a Quantum Dot



On the basis of Lee–Low–Pines unitary transformation, the influence of magnetic field and LO phonon effects on the energy of spin polarization states of strong-coupling bipolarons in a quantum dot (QD) is studied by using the variational method of Pekar type. The variations of the ground state energy \(E_0\) and the first excited state the energy \(E_1\) of bipolarons in a two-dimensional QD with the confinement strength of QDs \(\omega _0\), dielectric constant ratio \(\eta \), electron–phonon coupling strength \(\alpha \) and cyclotron resonance frequency of the magnetic field \(\omega _{c}\) are derived when the influence of the spin and external magnetic field is taken into account. The results show that both energies of the ground and first excited states (\(E_0\) and \(E_1)\) consist of four parts: the single-particle energy of electrons \(E_\mathrm{e}\), Coulomb interaction energy between two electrons \(E_\mathrm{c}\), interaction energy between the electron spin and magnetic field \(E_\mathrm{S}\) and interaction energy between the electron and phonon \(E_{\mathrm{e-ph}}\); the energy level of the first excited state \(E_1\) splits into two lines as \(E_1^{(1+1)}\) and \(E_1^{(1-1)}\) due to the interaction between the single-particle “orbital” motion and magnetic field, and each energy level of the ground and first excited states splits into three “fine structures” caused by the interaction between the electron spin and magnetic field; the value of \(E_{\mathrm{e-ph}}\) is always less than zero and its absolute value increases with increasing \(\omega _0\), \(\alpha \) and \(\omega _c\); the effect of the interaction between the electron and phonon is favorable to forming the binding bipolaron, but the existence of the confinement potential and Coulomb repulsive energy between electrons goes against that; the bipolaron with energy \(E_1^{(1-1)}\) is easier and more stable in the binding state than that with \(E_1^{(1+1)}\).


Quantum dot Bipolaron Spin polarization state LO phonon effects 



This work is supported by National Nature Science Foundation of Hebei Province, China (E2013407119) and the Items of Institution of Higher Education Scientific Research of Hebei Province, China (ZD20131008).


  1. 1.
    X.M. Dou, B.Q. Sun, D.S. Jiang, H.Q. Ni, Z.C. Niu, Phys. Rev. B 84, 033302 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    Z.W. Yan, Mod. Phys. Lett. B 19, 211 (2005)ADSCrossRefMATHGoogle Scholar
  3. 3.
    X.M. Dou, B.Q. Sun, S.S. Huang, H.Q. Ni, Z.C. Niu, Chin. Phys. Lett. 25, 501 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    Y.F. Huangfu, Z.W. Yan, Physica E 40(9), 2982 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    E. Chaolu, J.L. Xiao, J. Phys. Soc. Jpn. 76(4), 044702 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    E. Chaolu, W. Xin, Y.W. Zhao, Mod. Phys. Lett. B 24, 2705 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    E. Chaolu, W. Qimuge, X. Xiao, C. Han, W. Xin, Commun. Theor. Phys. 57, 157 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    F.L. Bloom, W. Wagemans, M. Kemerink, B. Koopmans, Appl. Phys. Lett. 93, 263302 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    J.D. Bergeson, V.N. Prigodin, D.M. Lincoln, A.J. Epstein, Phys. Rev. Lett. 100, 067201 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    L.Y. Xin, C.N. Li, F. Li, S.Y. Liu, B. Hu, Appl. Phys. Lett. 95, 123306 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    D. Emin, Phys. Rev. Lett. 62, 1544 (1989)ADSCrossRefGoogle Scholar
  12. 12.
    M. Hohenadler, P.B. Littlewood, Phys. Rev. B 76, 155122 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    L.C. Fai, A. Fomethe, A.J. Fotue, V.B. Mborong, S. Domngang, N. Issofa, M. Tchoffo, Superlattice. Microstruct. 43, 44 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    E. Chaolu, W. Xin, Physica B 406, 358 (2011)CrossRefGoogle Scholar
  15. 15.
    W. Xin, Z.M. Gao, W. Qimuge, C. Han, E. Chaolu, Superlattice. Microstruct. 52, 872 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    T.D. Lee, F.M. Low, D. Pines, Phys. Rev. 90, 97 (1953)ADSCrossRefMathSciNetGoogle Scholar
  17. 17.
    T. Yildirim, A. Ercelebi, J. Phys. Conden. Matter 3, 1271 (1999)ADSCrossRefGoogle Scholar
  18. 18.
    A. Chatterjee, Phys. Rev. B 41, 1668 (1990)ADSCrossRefGoogle Scholar
  19. 19.
    L. Schiff, Quantum Mechanics, 3rd edn. (McGraw-Hill, New York, 1968)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of Condensed Matter PhysicsHebei Normal University of Science and TechnologyQinhuangdaoChina
  2. 2.College of Physics and Electronic InformationInner Mongolia University for NationalitiesTongliaoChina

Personalised recommendations