{
  "id": "cond-mat/0101070",
  "version": "v1",
  "published": "2001-01-05T18:20:36.000Z",
  "updated": "2001-01-05T18:20:36.000Z",
  "title": "Numerical Study of the Localization-Delocalization Transition for Vibrations in Amorphous Silicon",
  "authors": [
    "William Garber",
    "Folkert M. Tangerman",
    "Philip B. Allen",
    "Joseph L. Feldman"
  ],
  "comment": "4 pages with 2 embedded postscript figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.mtrl-sci"
  ],
  "abstract": "Numerical studies of amorphous silicon in harmonic approximation show that the highest 3.5% of vibrational normal modes are localized. As vibrational frequency increases through the boundary separating localized from delocalized modes, near omega_c=70meV, (the \"mobility edge\") there is a localization-delocalization (LD) transition, similar to a second-order thermodynamic phase transition. By a numerical study on a system with 4096 atoms, we are able to see exponential decay lengths of exact vibrational eigenstates, and test whether or not these diverge at omega_c. Results are consistent with a localization length xi which diverges above omega_c as (omega-omega_c)^{-p} where the exponent is p = 1.3 +/- 0.5. Below the mobility edge we find no evidence for a diverging correlation length. Such an asymmetry would contradict scaling ideas, and we suppose it is a finite-size artifact. If the scaling regime is narrower than our 1 meV resolution, then it cannot be seen directly on our finite system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-01-05T18:20:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "numerical study",
      "amorphous silicon",
      "localization-delocalization transition",
      "vibrations",
      "mobility edge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001cond.mat..1070G"
    }
  }
}