Wave propagation and band tails of two-dimensional disordered systems in the thermodynamic limit

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Understanding the nature and formation of band gaps associated with the propagation of electromagnetic, electronic, or elastic waves in disordered materials as a function of system size presents fundamental and technological challenges. In particular, a basic question is whether band gaps in disordered systems exist in the thermodynamic limit. To explore this issue, we use a two-stage ensemble approach to study the formation of complete photonic band gaps (PBGs) for a sequence of increasingly large systems spanning a broad range of two-dimensional photonic network solids with varying degrees of local and global order, including hyperuniform and nonhyperuniform types. We discover that the gap in the density of states exhibits exponential tails and the apparent PBGs rapidly close as the system size increases for nearly all disordered networks considered. The only exceptions are sufficiently stealthy hyperuniform cases for which the band gaps remain open and the band tails exhibit a desirable power-law scaling reminiscent of the PBG behavior of photonic crystals in the thermodynamic limit.

Original languageEnglish (US)
Article numbere2213633119
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number52
StatePublished - Dec 27 2022

All Science Journal Classification (ASJC) codes

  • General


  • correlated disorder
  • finite-size effects
  • hyperuniformity
  • photonic band gaps
  • stealthy


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