  The extremely high thermal conductivity of graphene has received great
attention both in experiments and calculations. Obviously, new feature in
thermal properties is of primary importance for application of graphene-based
materials in thermal management in nanoscale. Here, we studied the thermal
conductivity of graphene helicoid, a newly reported graphene-related
nanostructure, using molecular dynamics simulation. Interestingly, in contrast
to the converged cross-plane thermal conductivity in multi-layer graphene,
axial thermal conductivity of graphene helicoid keeps increasing with thickness
with a power law scaling relationship, which is a consequence of the divergent
in-plane thermal conductivity of two-dimensional graphene. Moreover, the large
overlap between adjacent layers in graphene helicoid also promotes higher
thermal conductivity than multi-layer graphene. Furthermore, in the small
strain regime (< 10%), compressive strain can effectively increase the thermal
conductivity of graphene helicoid, while in the ultra large strain regime
(~100% to 500%), tensile strain does not decrease the heat current, unlike that
in generic solid-state materials. Our results reveal that the divergence in
thermal conductivity, associated with the anomalous strain dependence and the
unique structural flexibility, make graphene helicoid a new platform for
studying fascinating phenomena of key relevance to the scientific understanding
and technological applications of graphene-related materials.
