Eigen equation of super insulation materials

This paper presents a simple structure model of Super insulation Materials. According to the basic theory of atomic vibration wave propagation, the eigen equations of phonons in the metamaterials were deduced by the transfer matrix theory, the stress and amplitude continuity at the boundaries of different interval. A clear relationship of phonon frequency with atomic structure parameters and atomic characteristic parameters was detected. For some specifically designed metamaterials, no phonon vibration model can exists, which means that the materials cannot spread the hot phonons or effectively transfer heat, which is very meaningful for the study of new insulation materials.