Wavevector-dependent optical properties from wavevector-independent proper conductivity tensor

Abstract

We discuss the calculation of the refractive index by means of the ab initio scalar dielectric function and point out its inherent limitations. To overcome these, we start from the recently proposed fundamental, microscopic wave equation in materials in terms of the frequency- and wavevector-dependent dielectric tensor, and investigate under which conditions the standard treatment can be justified. Thereby, we address the question of neglecting the wavelength dependence of microscopic response functions. Furthermore, we analyze in how far the fundamental, microscopic wave equation is equivalent to the standard wave equation used in theoretical optics. In particular, we clarify the relation of the “effective” dielectric tensor used there to the microscopic dielectric tensor defined in ab initio physics.

Graphical abstract

References

  1. 1.

    G.A.H. Schober, R. Starke, Eur. Phys. J. B 91, 146 (2018); see also arXiv:1709.08811 [physics.class-ph]

    ADS  Article  Google Scholar 

  2. 2.

    G. Strinati, Riv. del Nuovo Cim. 11, 1 (1988)

    ADS  Article  Google Scholar 

  3. 3.

    W. Hanke, Adv. Phys. 27, 287 (1978)

    ADS  Article  Google Scholar 

  4. 4.

    F. Bechstedt, inMany-body approach to electronic excitations: concepts and applications, Springer Series in Solid-State Sciences (Springer-Verlag, Berlin/Heidelberg, 2015), Vol. 181

  5. 5.

    P.Y. Yu, M. Cardona,Fundamentals of semiconductors: physics and materials properties, Graduate Texts in Physics, 4th edn. (Springer-Verlag, Berlin/Heidelberg, 2010)

  6. 6.

    N.W. Ashcroft, N.D. Mermin,Solid state physics (Harcourt, Inc., Orlando, FL, 1976)

  7. 7.

    W. Schäfer, M. Wegener,Semiconductor optics and transport phenomena, Advanced Texts in Physics (Springer-Verlag, Berlin/Heidelberg, 2002)

  8. 8.

    D. Pines, P. Nozières,The theory of quantum liquids, Advanced Book Classics (Perseus Books Publishing, L. L. C., Cambridge, MA, 1999)

  9. 9.

    J.A. Berger, P.L. de Boeij, R. van Leeuwen, Phys. Rev. B 75, 035116 (2007)

    ADS  Article  Google Scholar 

  10. 10.

    J.S. Lee, G.A.H. Schober, M.S. Bahramy, H. Murakawa, Y. Onose, R. Arita, N. Nagaosa, Y. Tokura, Phys. Rev. Lett. 107, 117401 (2011)

    ADS  Article  Google Scholar 

  11. 11.

    L. Demkó, G.A.H. Schober, V. Kocsis, M.S. Bahramy, H. Murakawa, J.S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, Y. Tokura, Phys. Rev. Lett. 109, 167401 (2012)

    ADS  Article  Google Scholar 

  12. 12.

    H. Kawai, K. Yamashita, E. Cannuccia, A. Marini, Phys. Rev. B 89, 085202 (2014)

    ADS  Article  Google Scholar 

  13. 13.

    A.A. Makhnev, L.V. Nomerovannaya, T.V. Kuznetsova, O.E. Tereshchenko, K.A. Kokh, Opt. Spectrosc. 117, 764 (2014)

    ADS  Article  Google Scholar 

  14. 14.

    I.P. Rusinov, O.E. Tereshchenko, K.A. Kokh, A.R. Shakhmametova, I.A. Azarov, E.V. Chulkov, JETP Lett. 101, 507 (2015), [Pis’ma Zh. Eksp. Teor. Fiz. 101, 563 (2015)]

    ADS  Article  Google Scholar 

  15. 15.

    A. Akrap, J. Teyssier, A. Magrez, P. Bugnon, H. Berger, A.B. Kuzmenko, D. van der Marel, Phys. Rev. B 90, 035201 (2014)

    ADS  Article  Google Scholar 

  16. 16.

    G.M. Dongho Nguimdo, D.P. Joubert, Eur. Phys. J. B 88, 113 (2015)

    ADS  Article  Google Scholar 

  17. 17.

    L. Gracia, A. Beltran, D. Errandonea, Phys. Rev. B 80 (2009)

  18. 18.

    P. Löper, M. Stuckelberger, B. Niesen, J. Werner, M. Filipic, S.J. Moon, J.H. Yum, M. Topic, S. De Wolf, C. Ballif, J. Phys. Chem. Lett. 6, 66 (2015)

    Article  Google Scholar 

  19. 19.

    S. Saha, T.P. Sinha, A. Mookerjee, Phys. Rev. B 62, 8828 (2000)

    ADS  Article  Google Scholar 

  20. 20.

    M. Friedrich, W.G. Schmidt, A. Schindlmayr, S. Sanna, Phys. Rev. Materials 1, 054406 (2017)

    ADS  Article  Google Scholar 

  21. 21.

    S. Yamada, M. Noda, K. Nobusada, K. Yabana, Phys. Rev. B 98, 245147 (2018)

    ADS  Article  Google Scholar 

  22. 22.

    D. Sangalli, J.A. Berger, C. Attaccalite, M. Grüning, P. Romaniello, Phys. Rev. B 95, 155203 (2017)

    ADS  Article  Google Scholar 

  23. 23.

    D. Forcella, C. Prada, R. Carminati, Phys. Rev. Lett. 118, 134301 (2017)

    ADS  Article  Google Scholar 

  24. 24.

    R. Del Sole, E. Fiorino, Phys. Rev. B 29, 4631 (1984)

    ADS  Article  Google Scholar 

  25. 25.

    R. Starke, G.A.H. Schober, Photonics Nanostruct. Fundam. Appl. 14, 1 (2015); see also arXiv:1401.6800 [cond-mat.mtrl-sci]

    ADS  Article  Google Scholar 

  26. 26.

    R. Starke, G.A.H. Schober, Ab initio materials physics and microscopic electrodynamics of media, arXiv:1606.00445 [cond-mat.mtrl-sci] (2016)

  27. 27.

    R. Starke, G.A.H. Schober, Optik 140, 62 (2017); see also arXiv:1510.03404 [cond-mat.mtrl-sci]

    ADS  Article  Google Scholar 

  28. 28.

    G.F. Giuliani, G. Vignale,Quantum theory of the electron liquid (Cambridge University Press, Cambridge, 2005)

  29. 29.

    A. Altland, B. Simons,Condensed matter field theory, 2nd edn. (Cambridge University Press, Cambridge, 2010)

  30. 30.

    D.B. Melrose, inQuantum plasmadynamics: unmagnetized plasmas, Lecture Notes in Physics (Springer, New York, 2008), Vol. 735

  31. 31.

    Elk FP-LAPW Code, http://elk.sourceforge.net

  32. 32.

    R. Starke, G.A.H. Schober, Int. J. Mod. Phys. D 25, 1640010 (2016); see also arXiv:1409.3723 [math-ph]

    ADS  Article  Google Scholar 

  33. 33.

    R. Starke, G.A.H. Schober,Response Theory of the electron-phonon coupling, arXiv:1606.00012 [cond-mat.mtrl-sci] (2016)

  34. 34.

    R. Starke, G.A.H. Schober, Int. J. Mod. Phys. D 26, 1750163 (2017); see also arXiv:1702.06985 [physics.class-ph]

    ADS  Article  Google Scholar 

  35. 35.

    R. Starke, G.A.H. Schober, Phot. Nano. Fund. Appl. 26, 41 (2017); see also arXiv:1704.06615 [cond-mat.mtrl-sci]

    Article  Google Scholar 

  36. 36.

    G.A.H. Schober, R. Starke,General form of the full electromagnetic Green function in materials physics, arXiv:1704.07594 [physics.class-ph] (2017)

  37. 37.

    R. Starke, G.A.H. Schober, Optik 157, 275 (2018); see also arXiv:1705.11004 [physics.optics]

    ADS  Article  Google Scholar 

  38. 38.

    H. Bruus, K. Flensberg,Many-body quantum theory in condensed matter physics: an introduction (Oxford University Press, Oxford, 2004)

  39. 39.

    L.V. Keldysh, D.A. Kirzhnitz, A.A. Maradudin,The dielectric function of condensed systems, Modern Problems in Condensed Matter Sciences (Elsevier Science Publishers B.V., Amsterdam, 1989)

  40. 40.

    O.V. Dolgov, E.G. Maksimov, inThe dielectric function of condensed systems, Modern Problems in Condensed Matter Sciences, edited by L.V. Keldysh, D.A. Kirzhnitz, A.A. Maradudin (Elsevier Science Publishers B. V., Amsterdam, 1989)

  41. 41.

    L. Kantorovich,Quantum theory of the solid state: an introduction, Fundamental Theories of Physics (Springer Science+Business Media, Dordrecht, 2004)

  42. 42.

    R.M. Martin, Electronic structure: basic theory and practical methods (Cambridge University Press, Cambridge, 2008)

  43. 43.

    P.A. Martin, F. Rothen, Many-body problems and quantum field theory: an introduction (Springer-Verlag, Berlin/Heidelberg, 2002)

  44. 44.

    C. Vorwerk, C. Cocchi, C. Draxl, Comput. Phys. Commun. 201, 119 (2016)

    ADS  Article  Google Scholar 

  45. 45.

    H. Römer, Theoretical optics: an introduction (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005)

  46. 46.

    V.M. Agranovich, V.L. Ginzburg, inCrystal optics with spatial dispersion, and excitons, Springer Series in Solid-State Sciences, 2nd edn. (Springer-Verlag, Berlin/Heidelberg, 1984), Vol. 42

  47. 47.

    P.M. Platzmann, P.A. Wolff, Waves and interactions in solid state plasmas (Academic Press, New York/London, 1973)

  48. 48.

    D.B. Melrose, R.C. McPhedran, Electromagnetic processes in dispersive media: a treatment based on the dielectric tensor (Cambridge University Press, Cambridge, 1991)

  49. 49.

    V.G. Veselago, Sov. Phys. Usp. 10, 509 (1968)

    ADS  Article  Google Scholar 

  50. 50.

    M. Born, E. Wolf,Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, 7th edn. (Cambridge University Press, Cambridge, 1999)

  51. 51.

    A. Lipson, S.G. Lipson, H. Lipson,Optical Physics, 4th edn. (Cambridge University Press, Cambridge, 2011)

  52. 52.

    L.D. Landau, E.M. Lifshitz, inElectrodynamics of continuous media, Course of Theoretical Physics, 2nd edn. (Pergamon Press Ltd., Oxford, 1984), Vol. 8

  53. 53.

    A.K. Zvezdin, V.A. Kotov,Modern magnetooptics and magnetooptical materials, Studies in Condensed Matter Physics (IOP Publishing Ltd., Bristol, 1997)

  54. 54.

    M.M. Bredov, V.V. Rumyantsev, I.N. Toptygin, Klassicheskaya elektrodinamika (Nauka, Moscow, 1985)

  55. 55.

    L. Bergmann, C. Schaefer,Optics of waves and particles (Walter de Gruyter, Berlin, 1999)

  56. 56.

    G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996)

    ADS  Article  Google Scholar 

  57. 57.

    P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz,WIEN2k, an augmented plane wave + local orbitals program for calculating crystal properties (Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001)

  58. 58.

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo et al., J. Phys.: Condens. Matter 21, 395502 (2009)

    Google Scholar 

  59. 59.

    S. Schwalbe, R. Wirnata, R. Starke, G.A.H. Schober, J. Kortus, Phys. Rev. B 94, 205130 (2016)

    ADS  Article  Google Scholar 

Download references

Acknowledgments

Open access funding provided by Projekt Deal.

Author information

Affiliations

Authors

Corresponding author

Correspondence to René Wirnata.

Rights and permissions

Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Starke, R., Wirnata, R., Schober, G.A.H. et al. Wavevector-dependent optical properties from wavevector-independent proper conductivity tensor. Eur. Phys. J. B 93, 54 (2020). https://doi.org/10.1140/epjb/e2019-90569-0

Download citation

Keywords

  • Solid State and Materials