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

  • Atanu NandyEmail author
Regular Article
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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.

Graphical abstract

Keywords

Solid State and Materials 

Notes

Author contribution statement

I have done the entire work by myself.

References

  1. 1.
    P.W. Anderson, Phys. Rev. 109, 1492 (1958) ADSCrossRefGoogle Scholar
  2. 2.
    H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, B.A. Van Tiggelen, Nat. Phys. 4, 945 (2008) CrossRefGoogle Scholar
  3. 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) ADSCrossRefGoogle Scholar
  4. 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) ADSCrossRefGoogle Scholar
  5. 5.
    J.O. Vasseur, P.A. Deymier, G. Frantziskonis, G. Hong, B. Djafari-Rouhani, L. Dobrzynski, J. Phys.: Condens. Matter 10, 6051 (1998) ADSGoogle Scholar
  6. 6.
    I.O. Barinov, A.P. Alodzhants, S.M. Arakelyan, Quantum Electron. 39, 685 (2009) ADSCrossRefGoogle Scholar
  7. 7.
    D. Leykam, A. Andreanov, S. Flach, Adv. Phys. 3, 1473052 (2018) and the references therein Google Scholar
  8. 8.
    M. Hyrkäs, V. Apaja, M. Manninen, Phys. Rev. A 87, 023614 (2013) ADSCrossRefGoogle Scholar
  9. 9.
    S. Endo, T. Oka, H. Aoki, Phys. Rev. B 81, 113104 (2010) ADSCrossRefGoogle Scholar
  10. 10.
    A. Nandy, A. Chakrabarti, Phys. Rev. A 93, 013807 (2016) ADSCrossRefGoogle Scholar
  11. 11.
    A. Nandy, B. Pal, A. Chakrabarti, J. Phys.: Condens. Matter 27, 125501 (2015) ADSGoogle Scholar
  12. 12.
    B. Sutherland, Phys. Rev. B 34, 5208 (1986) ADSCrossRefGoogle Scholar
  13. 13.
    J. Vidal, R. Mosseri, B. Doucot, Phys. Rev. Lett. 81, 5888 (1998) ADSCrossRefGoogle Scholar
  14. 14.
    S. Mukherjee, M. Di Liberto, P. Öhberg, R.R. Thomson, N. Goldman, Phys. Rev. Lett. 121, 075502 (2018) ADSCrossRefGoogle Scholar
  15. 15.
    R.A. Vicencio, C. Mejía-Cortés, J. Opt. 16, 015706 (2014) ADSCrossRefGoogle Scholar
  16. 16.
    S. Xia, Y. Hu, D. Song, Y. Zong, L. Tang, Z. Chen, Opt. Lett. 41, 1435 (2016) ADSCrossRefGoogle Scholar
  17. 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) ADSCrossRefGoogle Scholar
  18. 18.
    J. von Neuman, E. Wigner, Phys. Z. 30, 467 (1929) Google Scholar
  19. 19.
    F.H. Stillinger, D.R. Herrick, Phys. Rev. A 11, 446 (1975) ADSCrossRefGoogle Scholar
  20. 20.
    M. Goda, S. Nishino, H. Matsuda, Phys. Rev. Lett. 96, 126401 (2006) ADSCrossRefGoogle Scholar
  21. 21.
    E.H. Lieb, Phys. Rev. Lett. 62, 1201 (1989) ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    A. Mielke, J. Phys. A 24, L73 (1991) ADSCrossRefGoogle Scholar
  23. 23.
    A. Mielke, J. Phys. A 24, 3311 (1991) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    H. Tasaki, Phys. Rev. Lett. 69, 1608 (1992) ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    A. Ramachandran, A. Andreanov, S. Flach, Phys. Rev. B 96, 161104(R) (2017) ADSCrossRefGoogle Scholar
  26. 26.
    A. Mielke, H. Tasaki, Commun. Math. Phys. 158, 341 (1993) ADSCrossRefGoogle Scholar
  27. 27.
    H. Tasaki, Prog. Theor. Phys. 99, 489 (1998) ADSCrossRefGoogle Scholar
  28. 28.
    E. Kapit, E. Mueller, Phys. Rev. Lett. 105, 215303 (2010) ADSCrossRefGoogle Scholar
  29. 29.
    E. Tang, J.-W. Mei, X.-G. Wen, Phys. Rev. Lett. 106, 236802 (2011) ADSCrossRefGoogle Scholar
  30. 30.
    K. Sun, Z. Gu, H. Katsura, S. Das Sarma, Phys. Rev. Lett. 106, 236803 (2011) ADSCrossRefGoogle Scholar
  31. 31.
    T. Neupert, L. Santos, C. Chamon, C. Mudry, Phys. Rev. Lett. 106, 236804 (2011) ADSCrossRefGoogle Scholar
  32. 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) ADSCrossRefGoogle Scholar
  33. 33.
    G.B. Wilson-Short, D.J. Singh, M. Fornari, M. Suewattana, Phys. Rev. B 75, 035121 (2007) ADSCrossRefGoogle Scholar
  34. 34.
    K. Kuroki, R. Arita, J. Phys. Soc. Jpn. 76, 083707 (2007) ADSCrossRefGoogle Scholar
  35. 35.
    R. Arita, K. Kuroki, K. Held, A.V. Lukoyanov, S. Skornyakov, V.I. Anisimov, Phys. Rev. B 78, 115121 (2008) ADSCrossRefGoogle Scholar
  36. 36.
    S. Mukherjee, R.R. Thomson, Opt. Lett. 40, 5443 (2015) ADSCrossRefGoogle Scholar
  37. 37.
    X. Cai, S. Chen, Y. Wang, Phys. Rev. A 87, 013607 (2013) ADSCrossRefGoogle Scholar
  38. 38.
    R. Khomeriki, S. Flach, Phys. Rev. Lett. 116, 245301 (2016) ADSCrossRefGoogle Scholar
  39. 39.
    S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, R.R. Thomson, Phys. Rev. Lett. 114, 245504 (2015) ADSCrossRefGoogle Scholar
  40. 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) ADSCrossRefGoogle Scholar
  41. 41.
    T. Baba, Nat. Photonics 2, 465 (2008) ADSCrossRefGoogle Scholar
  42. 42.
    L. Morales-Inostroza, R.A. Vicencio, Phys. Rev. A 94, 043831 (2016) ADSCrossRefGoogle Scholar
  43. 43.
    M. Röntgen, C.V. Morfonios, P. Schmelcher, Phys. Rev. B 97, 035161 (2018) ADSCrossRefGoogle Scholar
  44. 44.
    S. Flach, D. Leykam, J.D. Bodyfelt, P. Matthies, A.S. Desyatnikov, Europhys. Lett. 105, 30001 (2014) ADSCrossRefGoogle Scholar
  45. 45.
    W. Maimaiti, A. Andreanov, H.C. Park, O. Gendelman, S. Flach, Phys. Rev. B 95, 115135 (2017) ADSCrossRefGoogle Scholar
  46. 46.
    J.D. Bodyfelt, D. Leykam, C. Danieli, X. Yu, S. Flach, Phys. Rev. Lett. 113, 236403 (2014) ADSCrossRefGoogle Scholar
  47. 47.
    A. Nandy, A. Mukherjee, Phys. Lett. A 383, 2318 (2019) ADSCrossRefGoogle Scholar
  48. 48.
    S. Kirkpatrick, T.P. Eggarter, Phys. Rev. B 6, 3598 (1972) ADSCrossRefGoogle Scholar
  49. 49.
    Y. Liu, K.A. Chao, Phys. Rev. B 34, 5247 (1986) ADSCrossRefGoogle Scholar
  50. 50.
    H. Aoki, M. Ando, H. Matsumura, Phys. Rev. B 54, R17296 (1996) ADSCrossRefGoogle Scholar
  51. 51.
    N. Shima, H. Aoki, Phys. Rev. Lett. 71, 4389 (1993) ADSCrossRefGoogle Scholar
  52. 52.
    Z. Lan, N. Goldman, P. Öhberg, Phys. Rev. B 85, 155451 (2012) ADSCrossRefGoogle Scholar
  53. 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) CrossRefGoogle Scholar
  54. 54.
    M. Nità, B. Ostahie, A. Aldea, Phys. Rev. B 87, 125428 (2013) ADSCrossRefGoogle Scholar
  55. 55.
    H.-F. Cheung, Y. Gefen, E.K. Riedel, W.-H. Shih, Phys. Rev. B 37, 6050 (1988) ADSCrossRefGoogle Scholar
  56. 56.
    D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976) ADSCrossRefGoogle Scholar
  57. 57.
    E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987) ADSCrossRefGoogle Scholar
  58. 58.
    E. Yablonovitch, T.J. Gmitter, K.M. Leung, Phys. Rev. Lett. 67, 2295 (1991) ADSCrossRefGoogle Scholar
  59. 59.
    S. John, Phys. Rev. Lett. 58, 2486 (1987) ADSCrossRefGoogle Scholar
  60. 60.
    J.B. Pendry, A. MacKinon, Phys. Rev. Lett. 69, 2772 (1992) ADSCrossRefGoogle Scholar
  61. 61.
    S. Xia, Y. Hu, D. Song, Y. Zong, L. Tang, Z. Chen, Opt. Lett. 41, 1435 (2016) ADSCrossRefGoogle Scholar
  62. 62.
    Y. Zong, S. Xia, L. Tang, D. Song, Y. Hu, Y. Pei, J. Su, Y. Li, Z. Chen, Opt. Express 24, 8877 (2016) ADSCrossRefGoogle Scholar
  63. 63.
    S. Longhi, Opt. Lett. 39, 5892 (2014) ADSCrossRefGoogle Scholar
  64. 64.
    S. Longhi, Opt. Lett. 38, 3570 (2013) ADSCrossRefGoogle Scholar
  65. 65.
    S. Alexander, Phys. Rev. B 27, 1541 (1983) ADSMathSciNetCrossRefGoogle Scholar
  66. 66.
    Z.-Q. Zhang, P. Sheng, Phys. Rev. B 49, 83 (1994) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsKulti College, KultiPaschim BardhamanIndia

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