Anomalous size effect of thermal conductivity of two-dimensional dielectric materials

Abstract

In this work, we find that two-dimensional characteristics of hydrodynamic phonon transports in two-dimensional dielectric materials lead to the anomalous length dependency and even divergence of thermal conductivities. For suspended monolayer graphene the analytical solution of the two-dimensional Guyer-Krumhansl equations shows that the thermal conductivity increases with the increase of its length from 1 micron to 9 micron. When a specific temperature distribution at the inlet boundary is given, and the positive partial derivative of the heat flux along the length direction at the inlet and outlet boundaries is prescribed, analytical results show that the thermal conductivity of suspended monolayer graphene at the room temperature tends to infinity with the increase of its length. This result can be used to artificially regulate the thermal conductivity of suspended single-layer graphene.