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Robust flat band and flux induced engineering of dispersive band in a periodic lattice

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Abstract

We report the existence of flat band state in a periodic diamond dot lattice within the tight-binding framework. An analytical scheme to detect such non-dispersive state has been discussed elaborately. The dispersionless signature is clarified from the study of dispersion relation that is obtained by using real space renormalization group technique. The robustness of the flat band state with respect to the application of a uniform magnetic flux is analyzed along with the extensive numerical calculation of general spectral profile and two-channel transmission property. The amplitudes corresponding to this self-localized bound state are confined either within a finite size atomic cluster or pinned at a particular vertex making the particle immobile owing to the divergent effective mass. The challenging probability to engineer the band curvature (or equivalently the effective mass) using an external perturbation may inspire the experimentalists. The group velocity of the wave train can be manipulated (both in magnitude and sign) by virtue of the applied flux and hence the effective mass exhibits a re-entrant crossover as a function of the same external parameter.

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References

  1. P.W. Anderson, Phys. Rev. 109, 1492 (1958)

    ADS  Google Scholar 

  2. H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, B.A. Van Tiggelen, Nat. Phys. 4, 945 (2008)

    Google Scholar 

  3. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clèment, L. Sanchez-Palencia, P. Bouyer, A. Aspect, Nature (London) 453, 891 (2008)

    ADS  Google Scholar 

  4. A. Christ, Y. Ekinci, H.H. Solak, N.A. Gippius, S.G. Tikhodeev, O.J.F. Martin, Phys. Rev. B 76, 201405(R) (2007)

    ADS  Google Scholar 

  5. J.O. Vasseur, P.A. Deymier, G. Frantziskonis, G. Hong, B. Djafari-Rouhani, L. Dobrzynski, J. Phys.: Condens. Matter 10, 6051 (1998)

    ADS  Google Scholar 

  6. I.O. Barinov, A.P. Alodzhants, S.M. Arakelyan, Quantum Electron. 39, 685 (2009)

    ADS  Google Scholar 

  7. D. Leykam, A. Andreanov, S. Flach, Adv. Phys. 3, 1473052 (2018) and the references therein

    Google Scholar 

  8. M. Hyrkäs, V. Apaja, M. Manninen, Phys. Rev. A 87, 023614 (2013)

    ADS  Google Scholar 

  9. S. Endo, T. Oka, H. Aoki, Phys. Rev. B 81, 113104 (2010)

    ADS  Google Scholar 

  10. A. Nandy, A. Chakrabarti, Phys. Rev. A 93, 013807 (2016)

    ADS  Google Scholar 

  11. A. Nandy, B. Pal, A. Chakrabarti, J. Phys.: Condens. Matter 27, 125501 (2015)

    ADS  Google Scholar 

  12. B. Sutherland, Phys. Rev. B 34, 5208 (1986)

    ADS  Google Scholar 

  13. J. Vidal, R. Mosseri, B. Doucot, Phys. Rev. Lett. 81, 5888 (1998)

    ADS  Google Scholar 

  14. S. Mukherjee, M. Di Liberto, P. Öhberg, R.R. Thomson, N. Goldman, Phys. Rev. Lett. 121, 075502 (2018)

    ADS  Google Scholar 

  15. R.A. Vicencio, C. Mejía-Cortés, J. Opt. 16, 015706 (2014)

    ADS  Google Scholar 

  16. S. Xia, Y. Hu, D. Song, Y. Zong, L. Tang, Z. Chen, Opt. Lett. 41, 1435 (2016)

    ADS  Google Scholar 

  17. R.A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, M.I. Molina, Phys. Rev. Lett. 114, 245503 (2015)

    ADS  Google Scholar 

  18. J. von Neuman, E. Wigner, Phys. Z. 30, 467 (1929)

    Google Scholar 

  19. F.H. Stillinger, D.R. Herrick, Phys. Rev. A 11, 446 (1975)

    ADS  Google Scholar 

  20. M. Goda, S. Nishino, H. Matsuda, Phys. Rev. Lett. 96, 126401 (2006)

    ADS  Google Scholar 

  21. E.H. Lieb, Phys. Rev. Lett. 62, 1201 (1989)

    ADS  MathSciNet  Google Scholar 

  22. A. Mielke, J. Phys. A 24, L73 (1991)

    ADS  Google Scholar 

  23. A. Mielke, J. Phys. A 24, 3311 (1991)

    ADS  MathSciNet  Google Scholar 

  24. H. Tasaki, Phys. Rev. Lett. 69, 1608 (1992)

    ADS  MathSciNet  Google Scholar 

  25. A. Ramachandran, A. Andreanov, S. Flach, Phys. Rev. B 96, 161104(R) (2017)

    ADS  Google Scholar 

  26. A. Mielke, H. Tasaki, Commun. Math. Phys. 158, 341 (1993)

    ADS  Google Scholar 

  27. H. Tasaki, Prog. Theor. Phys. 99, 489 (1998)

    ADS  Google Scholar 

  28. E. Kapit, E. Mueller, Phys. Rev. Lett. 105, 215303 (2010)

    ADS  Google Scholar 

  29. E. Tang, J.-W. Mei, X.-G. Wen, Phys. Rev. Lett. 106, 236802 (2011)

    ADS  Google Scholar 

  30. K. Sun, Z. Gu, H. Katsura, S. Das Sarma, Phys. Rev. Lett. 106, 236803 (2011)

    ADS  Google Scholar 

  31. T. Neupert, L. Santos, C. Chamon, C. Mudry, Phys. Rev. Lett. 106, 236804 (2011)

    ADS  Google Scholar 

  32. T. Takeuchi, T. Kondo, T. Takami, H. Takahashi, H. Ikuta, U. Mizutani, K. Soda, R. Funahashi, M. Shikano, M. Mikami, S. Tsuda, T. Yokoya, S. Shin, T. Muro, Phys. Rev. B 69, 125410 (2004)

    ADS  Google Scholar 

  33. G.B. Wilson-Short, D.J. Singh, M. Fornari, M. Suewattana, Phys. Rev. B 75, 035121 (2007)

    ADS  Google Scholar 

  34. K. Kuroki, R. Arita, J. Phys. Soc. Jpn. 76, 083707 (2007)

    ADS  Google Scholar 

  35. R. Arita, K. Kuroki, K. Held, A.V. Lukoyanov, S. Skornyakov, V.I. Anisimov, Phys. Rev. B 78, 115121 (2008)

    ADS  Google Scholar 

  36. S. Mukherjee, R.R. Thomson, Opt. Lett. 40, 5443 (2015)

    ADS  Google Scholar 

  37. X. Cai, S. Chen, Y. Wang, Phys. Rev. A 87, 013607 (2013)

    ADS  Google Scholar 

  38. R. Khomeriki, S. Flach, Phys. Rev. Lett. 116, 245301 (2016)

    ADS  Google Scholar 

  39. S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, R.R. Thomson, Phys. Rev. Lett. 114, 245504 (2015)

    ADS  Google Scholar 

  40. R.A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, M.I. Molina, Phys. Rev. Lett. 114, 245503 (2015)

    ADS  Google Scholar 

  41. T. Baba, Nat. Photonics 2, 465 (2008)

    ADS  Google Scholar 

  42. L. Morales-Inostroza, R.A. Vicencio, Phys. Rev. A 94, 043831 (2016)

    ADS  Google Scholar 

  43. M. Röntgen, C.V. Morfonios, P. Schmelcher, Phys. Rev. B 97, 035161 (2018)

    ADS  Google Scholar 

  44. S. Flach, D. Leykam, J.D. Bodyfelt, P. Matthies, A.S. Desyatnikov, Europhys. Lett. 105, 30001 (2014)

    ADS  Google Scholar 

  45. W. Maimaiti, A. Andreanov, H.C. Park, O. Gendelman, S. Flach, Phys. Rev. B 95, 115135 (2017)

    ADS  Google Scholar 

  46. J.D. Bodyfelt, D. Leykam, C. Danieli, X. Yu, S. Flach, Phys. Rev. Lett. 113, 236403 (2014)

    ADS  Google Scholar 

  47. A. Nandy, A. Mukherjee, Phys. Lett. A 383, 2318 (2019)

    ADS  Google Scholar 

  48. S. Kirkpatrick, T.P. Eggarter, Phys. Rev. B 6, 3598 (1972)

    ADS  Google Scholar 

  49. Y. Liu, K.A. Chao, Phys. Rev. B 34, 5247 (1986)

    ADS  Google Scholar 

  50. H. Aoki, M. Ando, H. Matsumura, Phys. Rev. B 54, R17296 (1996)

    ADS  Google Scholar 

  51. N. Shima, H. Aoki, Phys. Rev. Lett. 71, 4389 (1993)

    ADS  Google Scholar 

  52. Z. Lan, N. Goldman, P. Öhberg, Phys. Rev. B 85, 155451 (2012)

    ADS  Google Scholar 

  53. H. Zhong, Y. Zhang, Y. Zhu, D. Zhang, C. Li, Y. Zhang, F. Li, M.R. Belić, M. Xiao, Ann. Phys. 529, 1600258 (2017)

    Google Scholar 

  54. M. Nità, B. Ostahie, A. Aldea, Phys. Rev. B 87, 125428 (2013)

    ADS  Google Scholar 

  55. H.-F. Cheung, Y. Gefen, E.K. Riedel, W.-H. Shih, Phys. Rev. B 37, 6050 (1988)

    ADS  Google Scholar 

  56. D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976)

    ADS  Google Scholar 

  57. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987)

    ADS  Google Scholar 

  58. E. Yablonovitch, T.J. Gmitter, K.M. Leung, Phys. Rev. Lett. 67, 2295 (1991)

    ADS  Google Scholar 

  59. S. John, Phys. Rev. Lett. 58, 2486 (1987)

    ADS  Google Scholar 

  60. J.B. Pendry, A. MacKinon, Phys. Rev. Lett. 69, 2772 (1992)

    ADS  Google Scholar 

  61. S. Xia, Y. Hu, D. Song, Y. Zong, L. Tang, Z. Chen, Opt. Lett. 41, 1435 (2016)

    ADS  Google Scholar 

  62. Y. Zong, S. Xia, L. Tang, D. Song, Y. Hu, Y. Pei, J. Su, Y. Li, Z. Chen, Opt. Express 24, 8877 (2016)

    ADS  Google Scholar 

  63. S. Longhi, Opt. Lett. 39, 5892 (2014)

    ADS  Google Scholar 

  64. S. Longhi, Opt. Lett. 38, 3570 (2013)

    ADS  Google Scholar 

  65. S. Alexander, Phys. Rev. B 27, 1541 (1983)

    ADS  MathSciNet  Google Scholar 

  66. Z.-Q. Zhang, P. Sheng, Phys. Rev. B 49, 83 (1994)

    ADS  Google Scholar 

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  1. Department of Physics, Kulti College, Kulti, Paschim Bardhaman, West Bengal-713 343, India

    Atanu Nandy

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  1. Atanu Nandy
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Nandy, A. Robust flat band and flux induced engineering of dispersive band in a periodic lattice. Eur. Phys. J. B 92, 213 (2019). https://doi.org/10.1140/epjb/e2019-100365-3

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