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Detection of boson peak and fractal dynamics of disordered system using terahertz spectroscopy

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 Added by Tatsuya Mori
 Publication date 2019
  fields Physics
and research's language is English




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Disordered systems exhibit universal excitation, referred to as the boson peak, in the terahertz region. Meanwhile, the so-called fracton is expected to appear in the nanoscale region owing to the self-similar structure of monomers in polymeric glasses. We demonstrate that such excitations can be detected using terahertz spectroscopy. For the interaction between terahertz light and the vibrational density of states of the fractal structure, we formulate an infrared light-vibration coupling coefficient for the fracton region. Accordingly, we show that information concerning fractal and fracton dimensions appears in the exponent of the absorption coefficient. Finally, using terahertz time-domain spectroscopy and low-frequency Raman scattering, we experimentally observe these universal excitations in a protein lysozyme system that has an intrinsically disordered and self-similar nature in a single supramolecule. These findings are applicable to disordered and polymeric glasses in general and will be key to understanding universal dynamics of disordered systems by terahertz light.



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We performed terahertz time-domain spectroscopy, low-frequency Raman scattering, and Brillouin light scattering on vitreous glucose to investigate the boson peak (BP) dynamics. In the spectra of {alpha}({ u})/{ u}2 [{alpha}({ u}) is the absorption coefficient], the BP is clearly observed around 1.1 THz. Correspondingly, the complex dielectric constant spectra show a universal resonancelike behavior only below the BP frequency. As an analytical scheme, we propose the relative light-vibration coupling coefficient (RCC), which is obtainable from the combination of the far-infrared and Raman spectra. The RCC reveals that the infrared light-vibration coupling coefficient CIR({ u}) of the vitreous glucose behaves linearly on frequency which deviates from Taraskins model of CIR({ u}) = A + B{ u}2 [S. N. Taraskin et al., Phys. Rev. Lett. 97, 055504 (2006)]. The linearity of CIR({ u}) might require modification of the second term of the model. The measured transverse sound velocity shows an apparent discontinuity with the flattened mode observed in the inelastic neutron scattering study [N. Violini et al., Phys. Rev. B 85, 134204 (2012)] and suggests a coupling between the transverse acoustic and flattened modes.
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We study a disordered vibrational model system, where the spring constants k are chosen from a distribution P(k) ~ 1/k above a cut-off value k_min > 0. We can motivate this distribution by the presence of free volume in glassy materials. We show that the model system reproduces several important features of the boson peak in real glasses: (i) a low-frequency excess contribution to the Debye density of states, (ii) the hump of the specific heat c_V(T) including the power-law relation between height and position of the hump, and (iii) the transition to localized modes well above the boson peak frequency.
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73 - W. Schirmacher , G Diezemann , 1998
We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(omega)/omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the boson peak, observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states.
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