Double-humped phonon resonance in doubly resonant vibration systems: Phonon metamaterials analogy with doubly resonant electromagnetic structures

Abstract

Phononic metamaterial which consists of two (or several) nanolayers separated by a planar defect of atomic-scale thickness is studied, under the assumption that the two-channel phonon interference mechanism of the transverse (cross-plane) heat flux control is dominant at high temperatures. An analytically exactly solvable discrete three-dimensional (3D) model of the multilayer interface between two semi-infinite bcc-lattice crystals is used to simulate phononic metamirror, metafilter, and meta-absorber. Two options of the general model in which two-path phonon interference reveals itself as double-humped resonance in the interface phonon absorption at weak dissipation or as total phonon transmission and total phonon reflection in the lossless limit are considered. An analogy is discussed between doubly resonant dissipative vibration systems and earlier investigated doubly resonant electromagnetic structure exhibiting both types of behavior: induced transparency and superscattering. It is shown that triple-peaked absorption resonance may arise from superposition of two-path phonon interference and Fabry-P\'erot-type interference in the system with triple defect layer. The existence conditions of double-peaked and triple-peaked resonances as well as total interface absorption are analyzed in terms of nondissipative phonon scattering properties and dissipative parameters. Also additional peculiarities relevant to the thermal interface resistance problem are described. The study provides insight into heat management in phononic nanostructures and metamaterials like metamirrors, metafilters, and meta-absorbers.