Smith-Chart-Driven Optimization of Bi₂Te₃ Single Crystal for Broadband Microwave Absorption

Originally devised as a nomograph for impedance matching design of alternating current circuits, the Smith chart has evolved into a universal compass for analyzing complex impedance in the radio-frequency domain. This study presents a detailed analysis of the significant potential of the Smith chart for impedance matching design in microwave absorbing field. Specifically, we demonstrate its utility as a real-time optimization guide. Topological insulators, owing to the high conductivity of their topological surface states, exhibit considerable advantages for microwave absorption. Herein, Bi₂Te₃ topological insulator single-crystal sheets were grown via spontaneous nucleation using a solid-state melting method and subsequently ground and dispersed in liquid paraffin to form homogeneous composites. By plotting the measured complex input impedance on the Smith chart, we continuously tracked the trajectory of the reflection coefficient. Crucially, instead of changing the material preparation process we adjusted the Bi₂Te₃ filling ratio to modulate the absorption bandwidth. An optimal mass ratio of Bi₂Te₃/paraffin was determined to be 80 wt% achieving an effective absorption bandwidth of 4.48 GHz, which is not only broader than most sheet-like Bi₂Te₃ materials reported before but also demonstrates the effectiveness of our approach. This work repositions the Smith chart from a passive impedance analysis tool to an active design optimization methodology, establishing a novel performance-oriented design paradigm for microwave absorbing materials that prioritizes target functionality over iterative synthesis.