Abstract
We discuss how the vibrational modes in an amorphous material can be characterized by various correlation functions. The spectrum of modes can be expected to contain both extended and localized states separated by mobility edges. The inverse participation ratio can be used as a measure of localization. To examine the vibrational modes in more detail, we propose to study moduli of Fourier transforms of powers of the eigenvector components. We have applied the analysis to vibrational modes of amorphous silicon. The structural and potential models that we use are based on the Wooten—Winer—Weaire bond-switching algorithm and Stillinger—Weber classical potential. The structural models are cubic supercells, periodically repeated. Whereas models ranging in size from 216 to 4096 atoms have been studied, only the 4096-atom model results are included here. In the analysis, we employ only q vectors that are consistent with the boundary conditions used to obtain the modes. Upon averaging over q-vector direction, systematic dependences result. The structural aspects of the model are briefly considered. In particular, no unusual structural ordering has been detected in the pair distribution function for the 4096-atom model.