Numerical study of the localization?delocalization transition for vibrations in amorphous silicon

• Published in: Philosophical magazine letters Vol. 81; no. 6; pp. 433 - 439
• Main Authors: Garber, William, Tangerman, Folkert M., Allen, Philip B., Feldman, Joseph L.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis Group 01.06.2001; Taylor & Francis
• Subjects: Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Lattice dynamics; Physics; Vibrational states in disordered systems; Phase transformations; Vibrational modes; Theoretical study; Numerical method; Silicon; Amorphous state; Localized modes
• ISSN: 0950-0839; 1362-3036
• DOI: 10.1080/09500830110041666

Numerical studies of amorphous Si in harmonic approximation show that the highest 3.5% of vibrational normal modes are localized. As the vibrational frequency increases through the boundary separating localized from delocalized modes, near omega sub(c) = 70 meV (the 'mobility edge') there is a localization-delocalization 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 to test whether or not these diverge at omega sub(c). Results are consistent with a localization length zeta which diverges above omega sub(c) as ( omega - omega sub(c)) super(-p) where the exponent is p approximately 1.3 plus or minus 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 artefact. If the scaling regime is narrower than our (approximately 1 meV) resolution, then it cannot be seen directly on our finite system.