We introduce and model a three-dimensional (3D) atomic-scale phononic metamaterial producing two-path phonon interference antiresonances to control the heat flux spectrum. We show that a crystal plane partially embedded with defect-atom arrays can completely reflect phonons at the frequency prescribed by masses and interaction forces. We emphasize the predominant role of the second phonon path and destructive interference in the origin of the total phonon reflection and thermal conductance reduction in comparison with the Fano-resonance concept. The random defect distribution in the plane and the anharmonicity of atom bonds do not deteriorate the antiresonance. The width of antiresonance dip can provide a measure of the coherence length of the phonon wave packet. All our conclusions are confirmed both by analytical studies of the equivalent quasi-1D lattice models and by numerical molecular dynamics (MD) simulations of realistic 3D lattices.Two-photon interference can result in a total cancellation of the photon output because of the coalescence of the two single photons, which was first observed by Hong et al. [1]. This interference effect occurs because two possible photon paths interfere destructively, which produces the famous "Hong-Ou-Mandel (HOM) dip" in the detection probability of the output photons. The HOM dip has since then been demonstrated in both the optical [2,3] and microwave[4] regime. In particular, two-photon destructive interference was recently demonstrated in a 3D optical metamaterial [5]. Similar destructive interference effect which results in a total reflection can be also realized in a phonon system. For the sound waves, the two-path phonon interference antiresonance was first described in Ref. [6], where the anomalous zero-transmission and total absorption of long-wavelength acoustic waves in a crystal with 2D (planar) defect were related with the destructive interf erence between the two possible phonon paths: through the nearest-neighbor bonds and through the non-nearest-neighbor bonds which couple directly crystal layers adjacent to the defect atomic plane.Constant endeavour has been devoted to the precisely control of heat conduction. Recent efforts concentrated on reducing the thermal conductivity κ via nanostructured materials with superlattices [7,8] and embedded nanoparticles [9][10][11]. Most works attributed the reduction of κ to the decreased phonon life time and thus the mean free path (MFP), which belong to the particle description of heat conduction. However, the role of destructive phonon interference in the reduction of κ is much less understood in the wave picture of thermal transport.In this Letter we introduce and model a realistic 3D atomic-scale phononic metamaterial that allows for manipulating the flow of thermal energy. Two-path phonon interference is generated by exploiting the phonon reflection on internal interfaces embedded with defect-atom arrays. The 2D planar defects force phonons to propagate through two paths: through unperturbed (matrix) and perturbed ...

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We introduce and model a three-dimensional atomic-scale phononic metamaterial producing two-path interference phonon antiresonances to control the heat flux spectrum. We show that a crystal plane partially filled with defect-atom arrays causes a total phonon reflection at the frequencies determined by masses and interaction forces. Such patterned atomic planes can be considered as high-finesse atomic-scale interference phonon metamirrors. We emphasize the predominant role of the second phonon path and destructive interference in the origin of the total reflection in comparison with the Fano-resonance concept. The random defect distribution in the plane and the anharmonicity of interatomic bonds do not deteriorate the interference antiresonances. The width of the interference antiresonance dip can provide a measure of the coherence length of the phonon wave packet. All our conclusions

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