{
  "id": "2406.16130",
  "version": "v1",
  "published": "2024-06-23T15:04:48.000Z",
  "updated": "2024-06-23T15:04:48.000Z",
  "title": "Wave functions in the Critical Phase: a Planar \\textit{Sierpiński} Fractal Lattice",
  "authors": [
    "Qi Yao",
    "Xiaotian Yang",
    "Askar A. Iliasov",
    "Mikhail I. Katsnelson",
    "Shengjun Yuan"
  ],
  "comment": "10 pages, 6 figures. Accepted by Phys. Rev. B",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.other"
  ],
  "abstract": "Electronic states play a crucial role in many quantum systems of moire superlattices, quasicrystals, and fractals. As recently reported in \\textit{Sierpi\\'{n}ski} lattices [Phys. Rev. B 107, 115424 (2023)], the critical states are revealed by the energy level-correlation spectra, which are caused by the interplay between aperiodicity and determined self-similarity characters. In the case of the \\textit{Sierpi\\'{n}ski Carpet}, our results further demonstrate that there is some degree of spatial overlap between these electronic states. These states could be strongly affected by its `seed lattice' of the $generator$, and slightly modulated by the dilation pattern and the geometrical self-similarity level. These electronic states are multifractal by scaling the $q$-order inverse participation ratio or fractal dimension, which correlates with the subdiffusion behavior. In the $gene$ pattern, the averaged state-based multifractal dimension of second-order would increase as its \\textit{Hausdoff dimension} increases. Our findings could potentially contribute to understanding quantum transports and single-particle quantum dynamics in fractals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-23T15:04:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractal lattice",
      "wave functions",
      "critical phase",
      "order inverse participation ratio",
      "energy level-correlation spectra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}