Numerical Study of the Localization-Delocalization Transition for Vibrations in Amorphous Silicon
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.
Keywords
Cite
@article{arxiv.cond-mat/0101070,
title = {Numerical Study of the Localization-Delocalization Transition for Vibrations in Amorphous Silicon},
author = {William Garber and Folkert M. Tangerman and Philip B. Allen and Joseph L. Feldman},
journal= {arXiv preprint arXiv:cond-mat/0101070},
year = {2007}
}
Comments
4 pages with 2 embedded postscript figures