Abstract

The so-called “phase difference” is commonly introduced as a phenomenological parameter in Raman tensor theory, so as to fit the experimental data well. Although phase difference is widely recognized as an intrinsic property of crystals, its physics still remains ambiguous. Recently, Kranert et al. have presented a new formalism to explain the origin of phase difference theoretically. Here, we systematically conducted experimental research with polar phonons in wurtzite crystals, the results of which strongly suggest that the phase difference should be predetermined in a Raman tensor, rather than be treated as Raman tensor elements traditionally or as an intrinsic property. On the grounds of pinpointing existing logical flaws in Raman tensor study, we provide a logically clear paradigm.

© 2018 Chinese Laser Press

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References

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  1. R. Loudon, “The Raman effect in crystals,” Adv. Phys. 13, 423–482 (1964).
    [Crossref]
  2. A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
    [Crossref]
  3. W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
    [Crossref]
  4. W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
    [Crossref]
  5. W. Zheng, R. S. Zheng, H. L. Wu, and F. D. Li, “Strongly anisotropic behavior of A1(TO) phonon mode in bulk AlN,” J. Alloys Compd. 584, 374–376 (2014).
    [Crossref]
  6. N. Djiedeu, B. Mohamadou, P. Bourson, and M. Aillerie, “Accurate determination of the anisotropy factors and the phase differences of Raman polarizabilities in some uniaxial crystals: the case of lithium niobate,” J. Phys. Condens. Matter 21, 015905 (2009).
    [Crossref]
  7. J. L. Yu, Y. F. Lai, Y. Z. Wang, S. Y. Cheng, and Y. H. Chen, “Polarized Raman scattering of single ZnO nanorod,” J. Appl. Phys. 115, 033505 (2014).
    [Crossref]
  8. H. C. Lin, Z. C. Feng, M. S. Chen, Z. X. Shen, I. T. Ferguson, and W. Lu, “Raman scattering study on anisotropic property of wurtzite GaN,” J. Appl. Phys. 105, 036102 (2009).
    [Crossref]
  9. T. Sander, S. Eisermann, B. K. Meyer, and P. J. Klar, “Raman tensor elements of wurtzite ZnO,” Phys. Rev. B 85, 165208 (2012).
    [Crossref]
  10. J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
    [Crossref]
  11. T. Livneh, J. Zhang, G. Cheng, and M. Moskovits, “Polarized Raman scattering from single GaN nanowires,” Phys. Rev. B 74, 035320 (2006).
    [Crossref]
  12. T. Strach, J. Brunen, B. Lederle, J. Zegenhagen, and M. Cardona, “Determination of the phase difference between the Raman tensor elements of the A1g-like phonons in SmBa2Cu3O7-delta,” Phys. Rev. B 57, 1292–1297 (1998).
    [Crossref]
  13. C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
    [Crossref]
  14. C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
    [Crossref]
  15. M. Cardona and G. Guntherodt, Light Scattering in Solid II (Springer, 1982).
  16. X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
    [Crossref]

2018 (1)

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

2016 (2)

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

2015 (3)

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
[Crossref]

W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
[Crossref]

2014 (2)

W. Zheng, R. S. Zheng, H. L. Wu, and F. D. Li, “Strongly anisotropic behavior of A1(TO) phonon mode in bulk AlN,” J. Alloys Compd. 584, 374–376 (2014).
[Crossref]

J. L. Yu, Y. F. Lai, Y. Z. Wang, S. Y. Cheng, and Y. H. Chen, “Polarized Raman scattering of single ZnO nanorod,” J. Appl. Phys. 115, 033505 (2014).
[Crossref]

2012 (1)

T. Sander, S. Eisermann, B. K. Meyer, and P. J. Klar, “Raman tensor elements of wurtzite ZnO,” Phys. Rev. B 85, 165208 (2012).
[Crossref]

2009 (2)

H. C. Lin, Z. C. Feng, M. S. Chen, Z. X. Shen, I. T. Ferguson, and W. Lu, “Raman scattering study on anisotropic property of wurtzite GaN,” J. Appl. Phys. 105, 036102 (2009).
[Crossref]

N. Djiedeu, B. Mohamadou, P. Bourson, and M. Aillerie, “Accurate determination of the anisotropy factors and the phase differences of Raman polarizabilities in some uniaxial crystals: the case of lithium niobate,” J. Phys. Condens. Matter 21, 015905 (2009).
[Crossref]

2006 (1)

T. Livneh, J. Zhang, G. Cheng, and M. Moskovits, “Polarized Raman scattering from single GaN nanowires,” Phys. Rev. B 74, 035320 (2006).
[Crossref]

2000 (1)

A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
[Crossref]

1998 (1)

T. Strach, J. Brunen, B. Lederle, J. Zegenhagen, and M. Cardona, “Determination of the phase difference between the Raman tensor elements of the A1g-like phonons in SmBa2Cu3O7-delta,” Phys. Rev. B 57, 1292–1297 (1998).
[Crossref]

1964 (1)

R. Loudon, “The Raman effect in crystals,” Adv. Phys. 13, 423–482 (1964).
[Crossref]

Aillerie, M.

N. Djiedeu, B. Mohamadou, P. Bourson, and M. Aillerie, “Accurate determination of the anisotropy factors and the phase differences of Raman polarizabilities in some uniaxial crystals: the case of lithium niobate,” J. Phys. Condens. Matter 21, 015905 (2009).
[Crossref]

Bourson, P.

N. Djiedeu, B. Mohamadou, P. Bourson, and M. Aillerie, “Accurate determination of the anisotropy factors and the phase differences of Raman polarizabilities in some uniaxial crystals: the case of lithium niobate,” J. Phys. Condens. Matter 21, 015905 (2009).
[Crossref]

Brunen, J.

T. Strach, J. Brunen, B. Lederle, J. Zegenhagen, and M. Cardona, “Determination of the phase difference between the Raman tensor elements of the A1g-like phonons in SmBa2Cu3O7-delta,” Phys. Rev. B 57, 1292–1297 (1998).
[Crossref]

Cardona, M.

T. Strach, J. Brunen, B. Lederle, J. Zegenhagen, and M. Cardona, “Determination of the phase difference between the Raman tensor elements of the A1g-like phonons in SmBa2Cu3O7-delta,” Phys. Rev. B 57, 1292–1297 (1998).
[Crossref]

M. Cardona and G. Guntherodt, Light Scattering in Solid II (Springer, 1982).

Chen, M. S.

H. C. Lin, Z. C. Feng, M. S. Chen, Z. X. Shen, I. T. Ferguson, and W. Lu, “Raman scattering study on anisotropic property of wurtzite GaN,” J. Appl. Phys. 105, 036102 (2009).
[Crossref]

Chen, Y. H.

J. L. Yu, Y. F. Lai, Y. Z. Wang, S. Y. Cheng, and Y. H. Chen, “Polarized Raman scattering of single ZnO nanorod,” J. Appl. Phys. 115, 033505 (2014).
[Crossref]

Cheng, G.

T. Livneh, J. Zhang, G. Cheng, and M. Moskovits, “Polarized Raman scattering from single GaN nanowires,” Phys. Rev. B 74, 035320 (2006).
[Crossref]

Cheng, S. Y.

J. L. Yu, Y. F. Lai, Y. Z. Wang, S. Y. Cheng, and Y. H. Chen, “Polarized Raman scattering of single ZnO nanorod,” J. Appl. Phys. 115, 033505 (2014).
[Crossref]

Cheong, H.

J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
[Crossref]

Dantas, M. S. S.

A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
[Crossref]

Djiedeu, N.

N. Djiedeu, B. Mohamadou, P. Bourson, and M. Aillerie, “Accurate determination of the anisotropy factors and the phase differences of Raman polarizabilities in some uniaxial crystals: the case of lithium niobate,” J. Phys. Condens. Matter 21, 015905 (2009).
[Crossref]

Dresselhaus, G.

A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
[Crossref]

Dresselhaus, M. S.

A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
[Crossref]

Eisermann, S.

T. Sander, S. Eisermann, B. K. Meyer, and P. J. Klar, “Raman tensor elements of wurtzite ZnO,” Phys. Rev. B 85, 165208 (2012).
[Crossref]

Feng, Z. C.

H. C. Lin, Z. C. Feng, M. S. Chen, Z. X. Shen, I. T. Ferguson, and W. Lu, “Raman scattering study on anisotropic property of wurtzite GaN,” J. Appl. Phys. 105, 036102 (2009).
[Crossref]

Ferguson, I. T.

H. C. Lin, Z. C. Feng, M. S. Chen, Z. X. Shen, I. T. Ferguson, and W. Lu, “Raman scattering study on anisotropic property of wurtzite GaN,” J. Appl. Phys. 105, 036102 (2009).
[Crossref]

Grundmann, M.

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

Guntherodt, G.

M. Cardona and G. Guntherodt, Light Scattering in Solid II (Springer, 1982).

Huang, F.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
[Crossref]

Ji, X.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Jiang, D.-S.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Jorio, A.

A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
[Crossref]

Kim, J.

J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
[Crossref]

Klar, P. J.

T. Sander, S. Eisermann, B. K. Meyer, and P. J. Klar, “Raman tensor elements of wurtzite ZnO,” Phys. Rev. B 85, 165208 (2012).
[Crossref]

Kranert, C.

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

Lai, Y. F.

J. L. Yu, Y. F. Lai, Y. Z. Wang, S. Y. Cheng, and Y. H. Chen, “Polarized Raman scattering of single ZnO nanorod,” J. Appl. Phys. 115, 033505 (2014).
[Crossref]

Lederle, B.

T. Strach, J. Brunen, B. Lederle, J. Zegenhagen, and M. Cardona, “Determination of the phase difference between the Raman tensor elements of the A1g-like phonons in SmBa2Cu3O7-delta,” Phys. Rev. B 57, 1292–1297 (1998).
[Crossref]

Lee, C.

J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
[Crossref]

Lee, J.

J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
[Crossref]

Lee, J.-U.

J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
[Crossref]

Lee, Z.

J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
[Crossref]

Li, F.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
[Crossref]

Li, F. D.

W. Zheng, R. S. Zheng, H. L. Wu, and F. D. Li, “Strongly anisotropic behavior of A1(TO) phonon mode in bulk AlN,” J. Alloys Compd. 584, 374–376 (2014).
[Crossref]

Li, G.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Liang, Y.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Lin, H. C.

H. C. Lin, Z. C. Feng, M. S. Chen, Z. X. Shen, I. T. Ferguson, and W. Lu, “Raman scattering study on anisotropic property of wurtzite GaN,” J. Appl. Phys. 105, 036102 (2009).
[Crossref]

Livneh, T.

T. Livneh, J. Zhang, G. Cheng, and M. Moskovits, “Polarized Raman scattering from single GaN nanowires,” Phys. Rev. B 74, 035320 (2006).
[Crossref]

Loudon, R.

R. Loudon, “The Raman effect in crystals,” Adv. Phys. 13, 423–482 (1964).
[Crossref]

Lu, W.

H. C. Lin, Z. C. Feng, M. S. Chen, Z. X. Shen, I. T. Ferguson, and W. Lu, “Raman scattering study on anisotropic property of wurtzite GaN,” J. Appl. Phys. 105, 036102 (2009).
[Crossref]

Meyer, B. K.

T. Sander, S. Eisermann, B. K. Meyer, and P. J. Klar, “Raman tensor elements of wurtzite ZnO,” Phys. Rev. B 85, 165208 (2012).
[Crossref]

Mohamadou, B.

N. Djiedeu, B. Mohamadou, P. Bourson, and M. Aillerie, “Accurate determination of the anisotropy factors and the phase differences of Raman polarizabilities in some uniaxial crystals: the case of lithium niobate,” J. Phys. Condens. Matter 21, 015905 (2009).
[Crossref]

Moskovits, M.

T. Livneh, J. Zhang, G. Cheng, and M. Moskovits, “Polarized Raman scattering from single GaN nanowires,” Phys. Rev. B 74, 035320 (2006).
[Crossref]

Park, H. J.

J. Kim, J.-U. Lee, J. Lee, H. J. Park, Z. Lee, C. Lee, and H. Cheong, “Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus,” Nanoscale 7, 18708–18715 (2015).
[Crossref]

Pimenta, M. A.

A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
[Crossref]

Qiao, X.-F.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Rao, A. M.

A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
[Crossref]

Saito, R.

A. M. Rao, A. Jorio, M. A. Pimenta, M. S. S. Dantas, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Polarized Raman study of aligned multiwalled carbon nanotubes,” Phys. Rev. Lett. 84, 1820–1823 (2000).
[Crossref]

Sander, T.

T. Sander, S. Eisermann, B. K. Meyer, and P. J. Klar, “Raman tensor elements of wurtzite ZnO,” Phys. Rev. B 85, 165208 (2012).
[Crossref]

Schmidt-Grund, R.

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

Shen, Z. X.

H. C. Lin, Z. C. Feng, M. S. Chen, Z. X. Shen, I. T. Ferguson, and W. Lu, “Raman scattering study on anisotropic property of wurtzite GaN,” J. Appl. Phys. 105, 036102 (2009).
[Crossref]

Shi, W.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Strach, T.

T. Strach, J. Brunen, B. Lederle, J. Zegenhagen, and M. Cardona, “Determination of the phase difference between the Raman tensor elements of the A1g-like phonons in SmBa2Cu3O7-delta,” Phys. Rev. B 57, 1292–1297 (1998).
[Crossref]

Sturm, C.

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

Tan, P.-H.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Wang, Y. Z.

J. L. Yu, Y. F. Lai, Y. Z. Wang, S. Y. Cheng, and Y. H. Chen, “Polarized Raman scattering of single ZnO nanorod,” J. Appl. Phys. 115, 033505 (2014).
[Crossref]

Wu, H.

Wu, H. L.

W. Zheng, R. S. Zheng, H. L. Wu, and F. D. Li, “Strongly anisotropic behavior of A1(TO) phonon mode in bulk AlN,” J. Alloys Compd. 584, 374–376 (2014).
[Crossref]

Wu, J.-B.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Yang, F.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Yu, J. L.

J. L. Yu, Y. F. Lai, Y. Z. Wang, S. Y. Cheng, and Y. H. Chen, “Polarized Raman scattering of single ZnO nanorod,” J. Appl. Phys. 115, 033505 (2014).
[Crossref]

Zegenhagen, J.

T. Strach, J. Brunen, B. Lederle, J. Zegenhagen, and M. Cardona, “Determination of the phase difference between the Raman tensor elements of the A1g-like phonons in SmBa2Cu3O7-delta,” Phys. Rev. B 57, 1292–1297 (1998).
[Crossref]

Zhang, J.

T. Livneh, J. Zhang, G. Cheng, and M. Moskovits, “Polarized Raman scattering from single GaN nanowires,” Phys. Rev. B 74, 035320 (2006).
[Crossref]

Zhang, X.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Zhang, Z.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Zheng, R.

Zheng, R. S.

W. Zheng, R. S. Zheng, H. L. Wu, and F. D. Li, “Strongly anisotropic behavior of A1(TO) phonon mode in bulk AlN,” J. Alloys Compd. 584, 374–376 (2014).
[Crossref]

Zheng, W.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
[Crossref]

W. Zheng, R. S. Zheng, H. L. Wu, and F. D. Li, “Strongly anisotropic behavior of A1(TO) phonon mode in bulk AlN,” J. Alloys Compd. 584, 374–376 (2014).
[Crossref]

ACS Nano (1)

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Figures (3)

Fig. 1.
Fig. 1. Angle-dependent polarized Raman spectra of AlN, GaN, ZnO, SiC bulk single crystals obtained on the m plane under a parallel polarization configuration for different rotation angles increasing from 0° to 180° with a step of 5°. The A1(TO), E1(TO), E22 phonons of each sample can be clearly identified. The parallel polarization configuration is written as X(αα)X¯ in shorthand, where X and X¯ denote the direction of propagation of incident and scattered lights, respectively; α represents the direction of polarization. Here, α=z·cosθ, in which θ is the angle between the polarization vector and the z axis.
Fig. 2.
Fig. 2. Fitted A1(TO) intensity-angle relationship of four wurtzite compounds using a traditional and a new Raman tensor, respectively. The “data” in the plot refers to the original experimental data, “Fitting 1” represents the fitting result using traditional theory, while “Fitting 2” represents the result of the new theory.
Fig. 3.
Fig. 3. Fitted phase differences and anisotropic ratios of wurtzite compounds using Eq. (3) as the Raman tensor.

Tables (1)

Tables Icon

Table 1. Raman Tensor Elements of Four Wurtzite Compounds Fitted from Angle-Dependent Polarized Raman Spectra Using Traditional and New Raman Tensor, Respectivelya

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

I|es·R[A1]·ei|2,
R[A1]=[|a|eiφa|a|eiφa|b|eiφb],
R[A1]=[|a||a||b|ei(φbφa)].
IA1||(θ)|a|2sin4θ+|b|2cos4θ+12|a||b|sin2(2θ)cosφab,
[|a||b|eiπ2],
[|a||a||b|eiπ2].
IA1(θ)|a|2sin4θ+|b|2cos4θ.
[aabeiϕ].
ϕ=arccos[f(δ,p1,p2,)],

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