Interplay of atomic-scale nonlinearity and nonhomogeneity in phonon transmittance and interface thermal conductance: Nonlinear and nonreciprocal phonon tunneling

The paper is devoted to analytical and numerical studies of phonon transmittance and thermal conductance through two-dimensional (2D) arrays of nonlinear atomic defects at the interfaces between different crystal lattices. The combination of nonhomogeneity (spatial asymmetry) of the structure and nonlinearity of atomic-scale scatterers can in general result in the nonreciprocity of phonon transmittance and interface thermal conductance (ITC). This phenomenon is caused by the generation of phonon second and third harmonics in the transmitted and reflected waves in the time-reversal system, as was predicted earlier by one of the authors [Yu. A. Kosevich, Phys. Rev. B 52, 1017 (1995)0163-182910.1103/PhysRevB.52.1017] and firmly confirmed in the present work in several interfaces with nonlinear atomic defects. In the present work, we consider interfaces with 2D arrays of atomic defects with different types of nonlinearity of interatomic bonds. Both one-path and two-path phonon transmission through 2D arrays of atomic defects are considered in spatially symmetric and asymmetric structures. It is shown that physically justified positive quartic nonlinearity enhances phonon transmittance and ITC. In contrast, the cubic nonlinearity, which is responsible for the thermal expansion of solids, can produce either a decrease or enhancement of the phonon transmittance and ITC depending on system parameters. It was found that in asymmetric systems, defect atoms oscillation amplitudes depend on the direction of phonon incidence, which leads to nonreciprocity of phonon transmittance and ITC due to cubic and/or quartic nonlinearity but does not violate reciprocity of phonon transmittance and ITC in linear systems. It is shown that the change in only the atomic mass in 2D array of atomic defects can significantly increase phonon transmittance and ITC through the interface between the lattices, strongly mismatched in atomic masses. The maximal value of the thermal conductance is reached for the optimal atomic defects mass at the given interface, when broad phonon total transmission resonance is realized. In the system with the optimal atomic defect mass, the interatomic bonds nonlinearity, either cubic or quartic, cannot increase phonon transmittance and ITC because the nonlinearity takes the system away from the optimal condition. Interfaces with the Si-Ge-like and diamond-copper-like atomic-mass mismatches are considered, and the corresponding optimal atomic defect masses are determined. Nonlinear and nonreciprocal phonon tunneling, which describes acoustic phonon transmission across the vacuum gap between two nonpiezoelectric solids (e.g., two metals), supported by the weak but long-range interaction between them as was predicted earlier by one of the authors [Yu. A. Kosevich, Phys. Lett. A 155, 295 (1991)0163-182910.1016/0375-9601(91)90487-S], is modeled and analyzed. Different types of nonlinearity of the weak coupling are considered in modeling of acoustic phonon tunneling and ITC in extreme near-field regime. The presented results contribute to better understanding and detailed modeling of the interplay between atomic-scale nonlinearity and nonhomogeneity in reciprocal and nonreciprocal phonon transmittance and ITC through 2D arrays of one-path and two-path nonlinear atomic defects with different topology.