Electrical and thermal transport in coplanar polycrystalline graphene-hBN heterostructures

We present a theoretical study of electronic and thermal transport in polycrystalline heterostructures combining graphene (G) and hexagonal boron nitride (hBN) grains of varying size and distribution. By increasing the hBN grain density from a few percents to $100\%$, the system evolves from a good conductor to an insulator, with the mobility dropping by orders of magnitude and the sheet resistance reaching the M$\Omega$ regime. The Seebeck coefficient is suppressed above $40\%$ mixing, while the thermal conductivity of polycrystalline hBN is found to be on the order of $30-120\,{\rm W}{\rm m}^{-1}{\rm K}^{-1}$. These results, agreeing with available experimental data, provide guidelines for tuning G-hBN properties in the context of two-dimensional materials engineering. In particular, while we proved that both electrical and thermal properties are largely affected by morphological features (like e.g. by the grain size and composition), we find in all cases that nm-sized polycrystalline G-hBN heterostructures are not good thermoelectric materials.