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Contact points open wide band gaps in all two-dimensional Bravais lattices

David Röhlig1,2,3,*, Ralf Zichner4,5, Thomas Blaudeck3,5, Angela Thränhardt2, and Vincent Laude1,†

  • *Contact author: david.rohlig@femto-st.fr
  • †Contact author: vincent.laude@femto-st.fr
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Phys. Rev. B 113, 144319 – Published 30 April, 2026

DOI: https://doi.org/10.1103/9ql7-t9rh

Abstract

The propagation of waves in crystals is known to be strongly affected by the choice and the spatial distribution of inclusions in a matrix. We argue herewith that in-contact, impermeable inclusions lead to extremely wide band gaps for all 2D Bravais lattices. Contact points entail constrictions that efficiently slow wave propagation and lead to strongly flattened bands. A numerical demonstration is provided for a generic Helmholtz equation that is applicable to electromagnetic, acoustic, elastic, or water waves alike. Experiments conducted on square and hexagonal photonic crystals composed of touching copper tubes reveal that waves of certain radio frequencies quite remarkably traverse the minute gaps within the metallic framework, thereby confirming the theoretical predictions, including the presence of deeply subwavelength Bragg band gaps.

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References (39)

  1. C. T. Chan, Essay: Photonic crystals as a platform to explore new physics, Phys. Rev. Lett. 135, 080001 (2025).
  2. M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Acoustic band structure of periodic elastic composites, Phys. Rev. Lett. 71, 2022 (1993).
  3. R. Martínez-Sala, J. Sancho, J. V. Sánchez, V. Gómez, J. Llinares, and F. Meseguer, Sound attenuation by sculpture, Nature (London) 378, 241 (1995).
  4. S. Brûlé, E. H. Javelaud, S. Enoch, and S. Guenneau, Experiments on seismic metamaterials: Molding surface waves, Phys. Rev. Lett. 112, 133901 (2014).
  5. M. Nomura, R. Anufriev, Z. Zhang, J. Maire, Y. Guo, R. Yanagisawa, and S. Volz, Review of thermal transport in phononic crystals, Mater. Today Phys. 22, 100613 (2022).
  6. S. Zhu, X. Zhao, L. Han, J. Zi, X. Hu, and H. Chen, Controlling water waves with artificial structures, Nat. Rev. Phys. 6, 231 (2024).
  7. S. Tacchi, G. Duerr, J. W. Klos, M. Madami, S. Neusser, G. Gubbiotti, G. Carlotti, M. Krawczyk, and D. Grundler, Forbidden band gaps in the spin-wave spectrum of a two-dimensional bicomponent magnonic crystal, Phys. Rev. Lett. 109, 137202 (2012).
  8. A. V. Chumak, V. S. Tiberkevich, A. D. Karenowska, A. A. Serga, J. F. Gregg, A. N. Slavin, and B. Hillebrands, All-linear time reversal by a dynamic artificial crystal, Nat. Commun. 1, 141 (2010).
  9. V. Laude, Local resonance and Fano resonance, Phononic Crystals (De Gruyter, Berlin, München, Boston, 2015), Chap. 10.1, pp. 303–327.
  10. W. H. Bragg, The reflection of x-rays by crystals. (II.), Proc. A 89, 246 (1913).
  11. Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, Locally resonant sonic materials, Science 289, 1734 (2000).
  12. R. T. Bonnecaze and J. Søndergaard Jensen, Systematic design of phononic band–gap materials and structures by topology optimization, Philos. Trans. R. Soc. Lond. Ser. A 361, 1001 (2003).
  13. J. Jensen and O. Sigmund, Topology optimization for nano-photonics, Laser Photon. Rev. 5, 308 (2011).
  14. W. Li, F. Meng, Y. Chen, Y. f. Li, and X. Huang, Topology optimization of photonic and phononic crystals and metamaterials: A review, Adv. Theor. Simul. 2, 1900017 (2019).
  15. J. Li, M. Qian, J. Yin, W. Lin, Z. Zhang, and S. Liu, Topology design of soft phononic crystals for tunable band gaps: A deep learning approach, Materials 18, 377 (2025).
  16. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Atlas of band gaps, Photonic Crystals (Princeton University Press, USA, 2008), pp. 242–251.
  17. Z.-f. Liu, B. Wu, and C. fu He, Band-gap optimization of two-dimensional phononic crystals based on genetic algorithm and fpwe, Waves Random Complex Medium 24, 286 (2014).
  18. G. Morales-Morales and J. Manzanares-Martinez, Enlargement of band gaps on thermal wave crystals by using heterostructures, Results Phys. 42, 106019 (2022).
  19. Z. Jia, Y. Chen, H. Yang, and L. Wang, Designing phononic crystals with wide and robust band gaps, Phys. Rev. Appl. 9, 044021 (2018).
  20. J. A. Iglesias Martínez, J. Moughames, G. Ulliac, M. Kadic, and V. Laude, Three-dimensional phononic crystal with ultra-wide bandgap at megahertz frequencies, Appl. Phys. Lett. 118, 063507 (2021).
  21. C. M. Reinke, M. F. Su, I. R. H. Olsson, and I. El-Kady, Realization of optimal bandgaps in solid-solid, solid-air, and hybrid solid-air-solid phononic crystal slabs, Appl. Phys. Lett. 98, 061912 (2011).
  22. M. S. Kushwaha, Stop-bands for periodic metallic rods: Sculptures that can filter the noise, Appl. Phys. Lett. 70, 3218 (1997).
  23. D. Caballero, J. Sánchez-Dehesa, C. Rubio, R. Mártinez-Sala, J. V. Sánchez-Pérez, F. Meseguer, and J. Llinares, Large two-dimensional sonic band gaps, Phys. Rev. E 60, R6316 (1999).
  24. D. Röhlig, E. Kuhn, F. Teichert, A. Thränhardt, and T. Blaudeck, Function phononic crystals, Europhys. Lett. 145, 26001 (2024).
  25. P. Lambin, A. Khelif, J. O. Vasseur, L. Dobrzynski, and B. Djafari-Rouhani, Stopping of acoustic waves by sonic polymer-fluid composites, Phys. Rev. E 63, 066605 (2001).
  26. Y. Liang, G. Yun, H. Yang, N. Bai, and Y. Cao, Dirac points and flat bands in two-dimensional magnonic crystals with honeycomb–kagome structure, AIP Adv. 14, 035242 (2024).
  27. D. Röhlig, A. Thränhardt, V. Laude, and T. Blaudeck, Giant band gaps in a phononic crystal with touching solid inclusions, Phys. Rev. Appl. 23, 054055 (2025).
  28. L. Tang, D. Song, S. Xia, S. Xia, J. Ma, W. Yan, Y. Hu, J. Xu, D. Leykam, and Z. Chen, Photonic flat-band lattices and unconventional light localization, Nanophoton. 9, 1161 (2020).
  29. L. Li, Use of fourier series in the analysis of discontinuous periodic structures, J. Opt. Soc. Am. A 13, 1870 (1996).
  30. H. S. Sözüer, J. W. Haus, and R. Inguva, Photonic bands: Convergence problems with the plane-wave method, Phys. Rev. B 45, 13962 (1992).
  31. R. Sainidou, N. Stefanou, I. Psarobas, and A. Modinos, A layer-multiple-scattering method for phononic crystals and heterostructures of such, Comput. Phys. Commun. 166, 197 (2005).
  32. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Three-dimensional photonic crystals, Photonic Crystals (Princeton University Press, USA, 2008), Chap. 6, pp. 94–121.
  33. W. Setyawan and S. Curtarolo, High-throughput electronic band structure calculations: Challenges and tools, Comput. Mater. Sci. 49, 299 (2010).
  34. F. Hecht, New development in freefem ++, J. Numer. Math. 20, 251 (2012).
  35. R. McPhedran, A. Movchan, and N. Movchan, Platonic crystals: Bloch bands, neutrality and defects, Mech. Mater. 41, 356 (2009).
  36. S. Brand, R. A. Abram, and M. A. Kaliteevski, Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods, Phys. Rev. B 75, 035102 (2007).
  37. F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, Wave propagation control at the deep subwavelength scale in metamaterials, Nat. Phys. 9, 55 (2013).
  38. D. Röhlig, V. Laude, R. Zichner, F. Thieme, A. Thränhardt, and T. Blaudeck, Radio wave attenuation by a large-scale photonic crystal sculpture, Sci. Rep. 15, 12317 (2025).
  39. V. Laude, Rigid cylinders in air, Phononic Crystals (De Gruyter, Berlin, München, Boston, 2015), Chap. 4.2.1, pp. 109–112.

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Phys. Rev. B 113, 144319– Published 30 April, 2026
  • Received 5 November 2025
  • Revised 20 January 2026
  • Accepted 2 April 2026
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