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. 2017 Jun 13;8:15843. doi: 10.1038/ncomms15843

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Copyright © 2017, The Author(s)

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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(a) Schematic picture of the trapezoid graphene. The angle θ=30° is close to that of the graphene sample #5. The big red arrow (plus direction J₊) indicates the direction with higher thermal conductivity, while the opposite direction (minus direction J-) has lower thermal conductivity. (b) The thermal rectification ratio versus the graphene width W₁ (angle θ is constant). The logarithmic curve-fitting gives y=−15.893 ln(x)+146.609 with R²=0.989. (c) Spatial energy distribution for the plus direction. (d) Spatial energy distribution for the minus direction. Here T_h and T_c denotes the high and low temperatures at two ends of graphene, and the spatial energy distribution includes those propagating phonon modes with the participation ratio larger than 0.4. The simulation results confirm that E₄<E₁, E₃<E₂, that is, local energy E of propagating modes is always smaller in case (d) than that in case (c) at both high-temperature and low-temperature ends.