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Casimir Effects in 2D Dirac Materials (Scientific Summary)

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Abstract

Fluctuation induced interactions originating from electromagnetic fields give rise to the Casimir force. Even though this is a universal interaction, because of the interplay between the response properties of interacting objects and their geometry the Casimir force can have many types of scaling laws, variations in magnitude and sign, and wide dependences on characteristic constants. The Casimir interaction is especially prominent in systems with reduced dimensions at micron and submicron scale separations. In recent years, examining this type of force for many nanostructured and chemically inert materials has become of great interest. Here, we review advances in the field of Casimir physics in the context of 2D layered materials with Dirac energy spectrum, such as graphene and related materials. The focus is on Casimir interactions and frictional effects with emphasis on the zero-point energy summation approach used for calculations. After giving an overview of this powerful technique, the optical response properties of graphene described with different models is presented. Numerical and analytical results in terms of characteristic behaviors for Casimir and Casimir-Polder interactions involving a stack of parallel layers are summarized. Other key results in the expanded graphene materials as well as their Casimir friction are also presented.

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References

  1. H. B. G. Casimir, Kon. Ned. Akad. Wetensch. Proc. 51, 793 (1948).

    Google Scholar 

  2. R. L. Jaffe, Phys. Rev. D 72, 021301 (2005).

    ADS  Google Scholar 

  3. H. B. G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948).

    ADS  Google Scholar 

  4. E. M. Lifshitz, Sov. Phys. JETP 2, 73 (1956).

    Google Scholar 

  5. L. M. Woods, D. A. R. Dalvit, A. Tkatchenko, P. Rodriguez-Lopez, A. W. Rodriguez, and R. Podgornik, Rev. Mod. Phys. 88, 45003 (2016).

    Google Scholar 

  6. D. Dalvit, P. Milonni, D. Roberts, and F. da Rosa, Casimir Physics (Springer, Berlin, Heidelberg, 2011).

    MATH  Google Scholar 

  7. G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009).

    ADS  Google Scholar 

  8. M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Effect (Oxford Univ. Press, Oxford, UK, 2009).

    MATH  Google Scholar 

  9. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. K. Otkevich, S. V. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. 102, 10451 (2005).

    ADS  Google Scholar 

  10. M. D. Stoller, S. Park, Z. Yanwu, J. A., and R. S. Ruoff, Nano Lett. 8, 3498 (2008).

    ADS  Google Scholar 

  11. Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and P. Avouris, Science (Washington, DC, U. S.) 327, 662 (2010).

    ADS  Google Scholar 

  12. B. Aïssa, N. K. Memon, A. Ali, and M. K. Khraisheh, Front. Mater. 2, 1 (2015).

    Google Scholar 

  13. A. Jorio, G. Dresselhaus, and M. S. Dresselhaus, Carbon Nanotubes, Advanced Topics in the Synthesis, Structure, Properties and Applications (Springer, Berlin, Heidelberg, 2008).

    MATH  Google Scholar 

  14. Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. Ron Shen, and F. Wang, Nature 459, 820 (2009).

    ADS  Google Scholar 

  15. V. L. Nguyen, D. J. Perello, S. Lee, C. T. Nai, B. G. Shin, J.-G. Kim, H. Y. Park, H. Y. Jeong, J. Zhao, Q. A. Vu, S. H. Lee, K. P. Loh, S.-Y. Jeong, and Y. H. Lee, Adv. Mater. 28, 8177 (2016).

    Google Scholar 

  16. H. Rydberg, M. Dion, N. Jacobson, E. Schroder, P. Hyldgaard, S. I. Simak, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 91, 126402 (2003).

    ADS  Google Scholar 

  17. J. Kleis and E. Schröder, J. Chem. Phys. 122, 192 (2005).

    Google Scholar 

  18. J. F. Dobson, A. White, and A. Rubio, Phys. Rev. Lett. 96, 73201 (2006).

    ADS  Google Scholar 

  19. M. Bordag, B. Geyer, G. L. Klimchitskaya, and V. M. Mostepanenko, Phys. Rev. B 74, 205431 (2006).

    ADS  Google Scholar 

  20. I. V. Bondarev and P. Lambin, Phys. Rev. B 72, 35451 (2005).

    ADS  Google Scholar 

  21. E. V. Blagov, G. L. Klimchitskaya, and V. M. Moste-panenko, Phys. Rev. B 75, 235413 (2007).

    ADS  Google Scholar 

  22. Yu. V. Churkin, A. B. Fedortsov, G. L. Klimchitskaya, and V. A. Yurova, Phys. Rev. B 82, 165433 (2010).

    ADS  Google Scholar 

  23. L. Henrard, E. Hernández, P. Bernier, and A. Rubio, Phys. Rev. B 60, R8521 (1999).

    ADS  Google Scholar 

  24. K. M. Liew, C. H. Wong, and M. J. Tan, Appl. Phys. Lett. 87, 041901 (2005).

    ADS  Google Scholar 

  25. A. Popescu, L. M. Woods, and I. V. Bondarev, Phys. Rev. B 83, 81406 (2011).

    ADS  Google Scholar 

  26. D. Drosdoff and L. M. Woods, Phys. Rev. Lett. 112, 025501 (2014).

    ADS  Google Scholar 

  27. A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune, and M. J. Heben, Nature (London, U.K.) 386, 377 (1997).

    ADS  Google Scholar 

  28. Yu. S. Nechaev, Phys. Usp. 49, 563 (2006).

    ADS  Google Scholar 

  29. N. Marom, J. Bernstein, J. Garel, A. Tkatchenko, E. Joselevich, L. Kronik, and O. Hod, Phys. Rev. Lett. 105, 046801 (2010).

    ADS  Google Scholar 

  30. J. F. Dobson, A. White, and A. Rubio, Phys. Rev. Lett. 96, 073201 (2006).

    ADS  Google Scholar 

  31. Ya. V. Shtogun and L. M. Woods, J. Phys. Chem. Lett. 1, 1356 (2010).

    Google Scholar 

  32. G. Barton, J. Phys. A Math. Gen. 38, 2997 (2005).

    ADS  Google Scholar 

  33. G. Barton, Proc. R. Soc. London, Ser. A 367, 117 (1979).

    ADS  Google Scholar 

  34. M. Bordag, J. Phys. A: Math. Gen. 39, 6173 (2006).

    ADS  Google Scholar 

  35. M. Bordag and N. Khusnutdinov, Phys. Rev. D 77, 85026 (2008).

    ADS  Google Scholar 

  36. G. L. Klimchitskaya and V. M. Mostepanenko, Phys. Rev. B 91, 45412 (2015).

    ADS  Google Scholar 

  37. M. Bordag, I. V. Fialkovsky, D. M. Gitman, and D. V. Vassilevich, Phys. Rev. B 80, 245406 (2009).

    ADS  Google Scholar 

  38. I. V. Fialkovsky, V. N. Marachevsky, and D. V. Vassilevich, Phys. Rev. B 84, 35446 (2011).

    ADS  Google Scholar 

  39. M. Bordag, I. Fialkovskiy, and D. Vassilevich, Phys. Rev. B 93, 75414 (2016).

    ADS  Google Scholar 

  40. M. Bordag, G. L. Klimchitskaya, and V. M. Mostepanenko, Phys. Rev. B 86, 165429 (2012).

    ADS  Google Scholar 

  41. M. Bordag, G. L. Klimchitskaya, V. M. Mostepanenko, and V. M. Petrov, Phys. Rev. D 91, 45037 (2015).

    ADS  Google Scholar 

  42. I. Fialkovsky and D. V. Vassilevich, Eur. Phys. J. B 85, 384 (2012).

    ADS  Google Scholar 

  43. D. Drosdoff and L. M. Woods, Phys. Rev. B 82, 155459 (2010).

    ADS  Google Scholar 

  44. D. Drosdoff, A. D. Phan, L. M. Woods, I. V. Bondarev, and J. F. Dobson, Eur. Phys. J. B 85, 365 (2012).

    ADS  Google Scholar 

  45. T. Stedman, D. Drosdoff, and L. M. Woods, Phys. Rev. A 89, 012509 (2014).

    ADS  Google Scholar 

  46. J. Sarabadani, A. Naji, R. Asgari, and R. Podgornik, Phys. Rev. B 84, 155407 (2011).

    ADS  Google Scholar 

  47. D. Drosdoff, I. V. Bondarev, A. Widom, R. Podgornik, and L. M. Woods, Phys. Rev. X 6, 011004 (2016).

    Google Scholar 

  48. D. Drosdoff and L. M. Woods, Phys. Rev. A 84, 062501 (2011).

    ADS  Google Scholar 

  49. A. A. Banishev, H. Wen, J. X., R. K. Kawakami, G. L. Klimchitskaya, V. M. Mostepanenko, and U. Mohideen, Phys. Rev. B 87, 205433 (2013).

    ADS  Google Scholar 

  50. G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Phys. Rev. B 89, 115419 (2014).

    ADS  Google Scholar 

  51. G. L. Klimchitskaya, V. M. Mostepanenko, and B. E. Sernelius, Phys. Rev. B 89, 125407 (2014).

    ADS  Google Scholar 

  52. H. B. G. Casimir, in Casimir Effect. 50 Years Later, Ed. by M. Bordag (World Scientific, Singapore, 1998), p. 3.

    Google Scholar 

  53. A. Lambrecht, P. A. Maia Neto, and S. Reynaud, New J. Phys. 8, 243 (2006).

    ADS  Google Scholar 

  54. A. Lambrecht and V. N. Marachevsky, Phys. Rev. Lett. 101, 160403 (2008).

    ADS  Google Scholar 

  55. S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Phys. Rev. D 80, 085021 (2009).

    ADS  Google Scholar 

  56. I. Fialkovsky, N. Khusnutdinov, and D. Vassilevich, Phys. Rev. B 97, 165432 (2018).

    ADS  Google Scholar 

  57. N. R. Khusnutdinov, Phys. Rev. B 83, 115454 (2011).

    ADS  Google Scholar 

  58. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, J. Phys.: Condens. Matter 19, 26222 (2007).

    Google Scholar 

  59. L. A. Falkovsky and A. A. Varlamov, Eur. Phys. J. B 56, 281 (2007).

    ADS  Google Scholar 

  60. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science (Washington, DC, U. S.) 320, 1308 (2008).

    ADS  Google Scholar 

  61. V. Zeitlin, Phys. Lett. B 352, 422 (1995).

    ADS  Google Scholar 

  62. I. V. Fialkovsky and D. V. Vassilevich, J. Phys. A: Math. Theor. 42, 442001 (2009).

    ADS  Google Scholar 

  63. I. V. Fialkovsky and D. V. Vassilevich, Int. J. Mod. Phys. A 27, 1260007 (2012).

    ADS  Google Scholar 

  64. N. Khusnutdinov, R. Kashapov, and L. M. Woods, 2D Mater. 5, 035032 (2018).

    Google Scholar 

  65. N. Khusnutdinov and N. Emelianova, Int. J. Mod. Phys. A 34, 1950008 (2019).

    ADS  Google Scholar 

  66. A. B. Djurišić and E. H. Li, J. Appl. Phys. 85, 7404 (1999).

    ADS  Google Scholar 

  67. N. Khusnutdinov, R. Kashapov, and L. M. Woods, Phys. Rev. D 92, 045002 (2015).

    ADS  Google Scholar 

  68. N. Khusnutdinov, D. Drosdoff, and L. M. Woods, Phys. Rev. D 89, 85033 (2014).

    ADS  Google Scholar 

  69. M. C. Schabel and J. L. Martins, Phys. Rev. B 46, 7185 (1992).

    ADS  Google Scholar 

  70. L. X. Benedict, N. G. Chopra, M. L. Cohen, A. Zettl, S. G. Louie, and V. H. Crespi, Chem. Phys. Lett. 286, 490 (1998).

    ADS  Google Scholar 

  71. R. Zacharia, H. Ulbricht, and T. Hertel, Phys. Rev. B 69, 155406 (2004).

    ADS  Google Scholar 

  72. N. Khusnutdinov, R. Kashapov, and L. M. Woods, Phys. Rev. A 94, 012513 (2016).

    ADS  Google Scholar 

  73. F. Zhou and L. Spruch, Phys. Rev. A 52, 297 (1995).

    ADS  Google Scholar 

  74. R. Kashapov, N. Khusnutdinov, and L. M. Woods, Int. J. Mod. Phys. A 31, 1641028 (2016).

    ADS  Google Scholar 

  75. N. Khusnutdinov, R. Kashapov, and L. M. Woods, in Physical and Mathematical Aspects of Symmetries, Proceedings of the 31st International Colloquium in Group Theoretical Methods in Physics (Springer Int., Cham, 2017), p. 203.

    MATH  Google Scholar 

  76. A. J. Mannix, B. Kiraly, M. C. Hersam, and N. P. Guisinger, Nat. Rev. Chem. 1, 0014 (2017).

    Google Scholar 

  77. M. Ezawa, Phys. Rev. Lett. 109, 055502 (2012).

    ADS  Google Scholar 

  78. M. Ezawa, J. Supercond. Novel Magn. 28, 1249 (2014).

    Google Scholar 

  79. P. Rodriguez-Lopez, W. J. M. Kort-Kamp, D. A. R. Dalvit, and L. M. Woods, Phys. Rev. Mater. 2, 014003 (2018).

    Google Scholar 

  80. P. Rodriguez-Lopez, W. J. M. Kort-Kamp, D. A. R. Dalvit, and L. M. Woods, Nat. Commun. 8, 1 (2017).

    Google Scholar 

  81. P. Rodriguez-Lopez and A. G. Grushin, Phys. Rev. Lett. 112, 056804 (2014).

    ADS  Google Scholar 

  82. W. K. Tse and A. H. MacDonald, Phys. Rev. Lett. 109, 236806 (2012).

    ADS  Google Scholar 

  83. A. I. Volokitin and B. N. J. Persson, Rev. Mod. Phys. 79, 1291 (2007).

    ADS  Google Scholar 

  84. T. J. Gramila, J. P. Eisenstein, A. H. MacDonald, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 66, 1216 (1991).

    ADS  Google Scholar 

  85. A. I. Volokitin and B. N. J. Persson, Phys. Rev. Lett. 106, 094502 (2011).

    ADS  Google Scholar 

  86. A. I. Volokitin and B. N. J. Persson, Phys. Rev. B 78, 155437 (2008).

    ADS  Google Scholar 

  87. A. I. Volokitin, JETP Lett. 104, 504 (2016).

    ADS  Google Scholar 

  88. M. B. Farias, C. D. Fosco, F. C. Lombardo, and F. D. Mazzitelli, Phys. Rev. D 95, 065012 (2017).

    ADS  MathSciNet  Google Scholar 

  89. M. B. Farias, W. J. M. Kort-Kamp, and D. A. R. Dalvit, Phys. Rev. B 97, 161407 (2018).

    ADS  Google Scholar 

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Funding

N. Khusnutdinov acknowledges the partial support of the São Paulo Research Foundation (FAPESP, grant nos. 2016/03319-6, 2017/50294-1, and 2019/10719-9) and the Russian Foundation for Basic Research (project no. 19-02-00496-a). L.M. Woods acknowledges the support of the US Department of Energy (grant no. DE-FG02-06ER46297).

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Authors and Affiliations

  1. Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170, Santo André, SP, Brazil

    N. Khusnutdinov

  2. Institute of Physics, Kazan Federal University, Kazan, 420008, Russia

    N. Khusnutdinov

  3. Department of Physics, University of South Florida, Tampa, Florida, 33620, USA

    L. M. Woods

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  1. N. Khusnutdinov
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Correspondence to N. Khusnutdinov.

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Khusnutdinov, N., Woods, L.M. Casimir Effects in 2D Dirac Materials (Scientific Summary). Jetp Lett. 110, 183–192 (2019). https://doi.org/10.1134/S0021364019150013

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