Extraordinary optical transmission was observed in metal films with periodic arrays of subwavelength holes and was related with the excitation of surface electromagnetic modes in the metal film. Here we demonstrate theoretically the realization of the extraordinary phonon transmission, which was predicted recently. We model the layered nanostructure of Ge atoms embedded in Si lattice, which contains a monolayer periodically filled with Ge and Si atoms, symmetrically encapsulated by the atomic-scale layers fully filled with Ge atoms. Such layered nanostructure demonstrates narrow transmission peak in THz frequency range on very low transmission background. The extraordinary phonon transmission occurs through the hidden lattice-wave nanochannels, which are provided by the host Si atoms embedded in the layer of defect Ge atoms which act as effective heavy isotopes in a diamond Si lattice. The encapsulated light Si atoms provide the narrow atomic vibrational eigenmode on almost zero vibrational background of surrounding heavy isotopes through which the resonance quantum phonon tunneling occurs.
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