Resolving anomalous strain effects on two-dimensional phonon flows: The cases of graphene, boron nitride, and planar superlattices

The physics of thermal transport on strained, two-dimensional (2D) materials graphene, boron nitride, and their superlattices is analyzed by molecular dynamics, lattice dynamics, and numerical solutions to Boltzmann transport equation. The thermal conductivity of thesematerials is found to be highly sensitive to tensile strain, and the strain dependence itself is also highly dependent on the sample total length. Both finite-sized systems (varying from similar to 100 to 300 nm long) as well as infinitely long systems are considered. In contrast to the typical reduction of thermal conductivity with strain exhibited by bulk 3D materials, the thermal conductivity initially increases to a peak value, after which it then decreases with further strain. Modal decomposition of the phonon spectrum shows that the nonmonotonic behavior arises from a competition between in-plane softening and flexural stiffening of phonons. The length sensitivity arises from the nature of the linear/quadratic dispersion of the in-plane/flexural modes and their distinct scattering selection rules: longer systems favor out-of-plane flexural phonon stiffening while smaller systems favor in-plane phonon softening. Additionally, we show that this competition occurs in concert with a strain-induced transition in the nature of the phonon flow from ballistic dominant to diffusive dominant. Overall these effects give rise to a complex dependence of thermal conductivity on strain and sample size.