Abstract
In order to study the vibrational properties of harmonic disordered solids we consider two models for disorder: Randomly fluctuating elastic constants (intrinsic disorder) and coupling to local oscillators (defects) with random eigen frequencies. The first model is treated in self-consistent Born approximation (SCBA), whereas the second can be solved exactly. This enables us to discuss the accuracy of the SCBA. In both models an enhancement of the low-frequency vibrational density of states over that predicted by Debye is obtained (”boson peak”) as a result of the presence of the disorder. In the frequency regime above the boson peak an almost exponential decrease of the reduced density of states is obtained, which is widely observed in experiments. Whereas the gross features of the models are similar, the details can be different, depending on the model parameters chosen.
It is argued that models involving intrinsic disorder are suitable for structurally disordered solids, whereas defect models seem more adequate for disordered crystals.
PACS number: 65.60.+a
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Maurer, E., Schirmacher, W. Local Oscillators vs. Elastic Disorder: A Comparison of Two Models for the Boson Peak. Journal of Low Temperature Physics 137, 453–470 (2004). https://doi.org/10.1023/B:JOLT.0000049065.04709.3e
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DOI: https://doi.org/10.1023/B:JOLT.0000049065.04709.3e