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Journal of the Korean Physical Society

, Volume 60, Issue 3, pp 403–409 | Cite as

Application of block diagonal technique to a Hamiltonian matrix in performing spin-splitting calculations for GaN wurtzite materials

  • Chun-Nan Chen
  • Sheng-Hsiung Chang
  • Wei-Long Su
  • Wan-Tsang Wang
  • Hsiu-Fen Kao
  • Jen-Yi Jen
  • Yiming Li
Article
  • 63 Downloads

Abstract

The bulk inversion asymmetry (Dresselhaus) terms (i.e., B 2, B 1, and B1 terms) of wurtzite materials are determined. The 2 × 2 conduction band, 2 × 2 heavy-hole band, 2 × 2 light-hole band, and 2 × 2 crystal-field split-off hole band matrices of wurtzite semiconductors are developed and decoupled by using a block diagonal technique. Importantly, those 2 × 2 block diagonal matrices incorporate not only the interband coupling effect but also the bulk inversion asymmetry effect. Analytical expressions for the conduction and the valence band spin-splitting parameters and energies of GaN wurtzite materials are formulated by solving the block diagonal matrices. The presence of these terms is shown to include the spin-splitting phenomenon.

Keywords

Spin splitting Inversion asymmetry GaN Dresselhaus Wurtzite 

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References

  1. [1]
    G. Prinz, Science 282, 1660 (1998).CrossRefGoogle Scholar
  2. [2]
    S. D. Sarma, Am. Sci. 89, 516 (2001).ADSGoogle Scholar
  3. [3]
    S. A. Wolf and D. Treger, IEEE Trans. Magn. 36, 2748 (2000).ADSCrossRefGoogle Scholar
  4. [4]
    P. Pfeffer and W. Zawadzki, Phys. Rev. B 72, 035325 (2005).ADSCrossRefGoogle Scholar
  5. [5]
    L. Jiang and M. W. Wu, Phys. Rev. B 72, 033311 (2005).ADSCrossRefGoogle Scholar
  6. [6]
    G. Bastaau]rd, Phys. Rev. B 46, 4253 (1992).ADSCrossRefGoogle Scholar
  7. [7]
    H. L. Störmer, Z. Schlesinger, A. Chang, D. C. Tsui, A. C. Gossard and W. Wiegmann, Phys. Rev. Lett. 51, 126 (1983).ADSCrossRefGoogle Scholar
  8. [8]
    J. P. Eisenstein, H. L. Störmer, U. Narayanaumurti, A. C. Gossard and W. Wiegmann, Phys. Rev. Lett. 53, 2579 (1984).ADSCrossRefGoogle Scholar
  9. [9]
    I. Žutić, J. Fabian and S. D. Sarma, Rev. Mod. Phys. 76, 323 (2004).ADSCrossRefGoogle Scholar
  10. [10]
    I. Lo, M. H. Gau, J. K. Tsai, Y. L. Chen, Z. J. Chang, W. T. Wang, J. C. Chiang, T. Aggerstam and S. Lourdudoss, Phys. Rev. B 75, 245307 (2007).ADSCrossRefGoogle Scholar
  11. [11]
    D. D. Awschalom, D. Loss and N. Samarth, Semiconductor Spintronics and Quantum Computation (Springer-Verlag Publications, Berlin, 2002).Google Scholar
  12. [12]
    G. Dresselhaus, Phys. Rev. 100, 580 (1955).ADSzbMATHCrossRefGoogle Scholar
  13. [13]
    Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).ADSCrossRefGoogle Scholar
  14. [14]
    B. Beschoten et al., Phys. Rev. B 63, 121202 (R) (2001).ADSCrossRefGoogle Scholar
  15. [15]
    J. H. Buss, J. Rudolph, F. Natali, F. Semond and D. Hagele, Phys. Rev. B 81, 155216 (2010).ADSCrossRefGoogle Scholar
  16. [16]
    I. Lo et al., Phys. Rev. B 65, 161306 (2002).ADSCrossRefGoogle Scholar
  17. [17]
    C. N. Chen et al., J. Appl. Phys. 104, 024901 (2008).ADSCrossRefGoogle Scholar
  18. [18]
    C. N. Chen, Y. H. Wang, M. P. Houng and J. C. Chiang, Jpn. J. Appl. Phys., Part 1 41, 36 (2002).CrossRefGoogle Scholar
  19. [19]
    W. A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond (Dover Publications, New York, 1989).Google Scholar
  20. [20]
    A. Kobayashi, O. F. Sankey, S. M. Volz and J. D. Dow, Phys. Rev. B 28, 935 (1983).ADSCrossRefGoogle Scholar
  21. [21]
    C. N. Chen, Phys. Rev. B 72, 085305 (2005).ADSCrossRefGoogle Scholar
  22. [22]
    C. N. Chen, J. Appl. Phys. 96, 7374 (2004).ADSCrossRefGoogle Scholar
  23. [23]
    C. N. Chen, S. H. Chang, M. L. Hung, J. C. Chiang, I. Lo, W. T. Wang, M. H. Gau, H. F. Kao and M. E. Lee, J. Appl. Phys. 101, 043104 (2007).ADSCrossRefGoogle Scholar
  24. [24]
    Y. C. Chang, Phy. Rev. B 37, 8215 (1988).ADSCrossRefGoogle Scholar
  25. [25]
    S. L. Chuang and C. S. Chang, Phys. Rev. B 54, 2491 (1996).ADSCrossRefGoogle Scholar
  26. [26]
    D. W. Jenkins and J. D. Dow, Phys. Rev. B 39, 3317 (1996).ADSCrossRefGoogle Scholar
  27. [27]
    E. O. Kane, Semiconductors and Semimetals, edited by R. K. Willardson and A. C. Beer (Academic Press, New York, 1966), Vol. 1, p. 75.CrossRefGoogle Scholar
  28. [28]
    C. N. Chen, S. H. Chang, M. E. Lee, J. C. Chiang, I. Lo, W. T. Wang, M. H. Gau and H. F. Kao, J. Appl. Phys. 101, 046105 (2007).ADSCrossRefGoogle Scholar
  29. [29]
    W. T. Wang et al., Appl. Phys. Lett. 91, 082110 (2007).ADSCrossRefGoogle Scholar
  30. [30]
    C. M. Yin, B. Shen, Q. Zhang, F. J. Xu, N. Tang, L. B. Cen, X. Q. Wang, Y. H. Chen and J. L. Yu, Appl. Phys. Lett. 97, 181904 (2010).ADSCrossRefGoogle Scholar
  31. [31]
    M. W. Wu, J. H. Jiang and M. Q. Weng, Phys. Rep. 493, 61 (2010).MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    E. L. Ivchenko and G. E. Pikus, Superlattices and Other Heterostructures (Springer-Verlag, Berlin, 1995), Chap. 3.CrossRefGoogle Scholar

Copyright information

© The Korean Physical Society 2012

Authors and Affiliations

  • Chun-Nan Chen
    • 1
  • Sheng-Hsiung Chang
    • 2
  • Wei-Long Su
    • 3
  • Wan-Tsang Wang
    • 4
  • Hsiu-Fen Kao
    • 4
  • Jen-Yi Jen
    • 1
  • Yiming Li
    • 5
  1. 1.Quantum Engineering Laboratory, Department of PhysicsTamkang UniversityTamsui Town, TaipeiTaiwan
  2. 2.Department of Optoelectronic EngineeringFar-East UniversityHsin-Shih Town, TainanTaiwan
  3. 3.Department of Digital Mulitimedia TechnologyLee-Ming Institute of TechnologyTai-Shan, TaipeiTaiwan
  4. 4.Department of PhysicsNational Sun Yat-Sen UniversityKaohsiungTaiwan
  5. 5.Department of Electrical EngineeringNational Chiao Tung UniversityHsinchuTaiwan

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