The minimum thermal conductance versus supercell size ($d_{ s}$) is revealed in graphene and boron nitride superlattice with $d_{ s}$ far below the phonon mean free path. The minimum value is reached at a constant ratio of $d_{ s}/L\approx 5%$, where $L$ is the total length of the superlattice; thus the minimum point of $d_{ s}$ depends on $L$. The phenomenon is attributed to the localization property and the number of confined modes in the superlattice. With the increase of $d_{ s}$, the localization of the confined mode is enhanced while the number of confined modes decreases, which directly results in the minimum thermal conductance.
Categories: cond-mat.mtrl-sci