Shaped graded materials with an apparent negative thermal conductivity

Based on a first-principles approach, we exploit a class of shaped graded materials in which thermal energy is apparently controlled to transfer from a region of lower temperature to a region of higher temperature. This phenomenon, which is in contrast to our common intuition, is indicative of an apparent negative thermal conductivity (ANTC). Further analysis shows that the ANTC is related to a symmetric oscillation of paired thermal conductivities with specific gradation profiles, which are shown to satisfy a sum rule. Such shaped graded materials can serve as good candidates for thermal rectification.