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.
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