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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