Minimum thermal conductance in graphene and boron nitride superlattice

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 $d_s\mathrm{/}L\approx 5$, 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.