The boson peak is a largely unexplained excitation found universally in the terahertz vibrational spectra of disordered systems; the so-called fracton is a vibrational excitation associated with the self-similar structure of monomers in polymeric glasses. We demonstrate that such excitations can be detected using terahertz spectroscopy. In the case of fractal structures, we determine the infrared light-vibration coupling coefficient for the fracton region and show that information concerning the 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 fractal structure and argue that the system should be considered a single supramolecule. These findings are applicable to amorphous and fractal objects in general and will be valuable for understanding universal dynamics of disordered systems via terahertz light.

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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