TE materials have been studied and developed for 200 years since the Seebeck effect was discovered in 1821. Due to the promising applications of TE materials in waste heat power generation and solid-state refrigeration, persistent efforts have been made to improve TE performance. The best TE materials at present, such as Bi2Te3, PbTe, GeTe, and CoSb, are all heavily-doped narrow-bandgap semiconductors. In addition, reliably reproducible zT is around 2.0, the reported zT values above 2.0 are often in debate, and all belong to heavily-doped narrow-bandgap semiconductors. Therefore, it seems desperately needed to break through the limitation of narrow-bandgap semiconductors for discovering high-performance TE materials. In this work, a team led by Prof. Jun Luo from Shanghai University and Prof. Wenqing Zhang from Southern University of Science and Technology, demonstrated that a few Heusler-like materials, TiFexCu2x？1Sb (x？=？0.70, 0,75, 0.80) and TiFe1.33Sb, show peculiar NFL metallic transport together with promising TE performance. The study revealed that the NFL metal showing a quantum critical behavior may be a type of high-performance TE material. The random filling of Fe/Cu atoms on the equivalent 4c/4d sites of the Heusler metals TiFexCu2x？1Sb and TiFe1.33Sb, leads to the structure disorder, strong magnetic fluctuation, and quantum critical behavior of these non-conventional metals. The Seebeck coefficient of TiFexCu2x？1Sb and TiFe1.33Sb increases continuously with the increase of temperature, while a low resistivity is maintained at the same time. Combined with the very low thermal conductivity due to the disordered structure, the TiFexCu2x？1Sb and TiFe1.33Sb samples achieve the TE performance comparable to or even better than the traditional TE semiconductors. Among them, the TiFe0.7Cu0.4Sb sample shows a Seebeck coefficient of 194 V/K at 700？K and a zT value of 0.75 at 973？K, suggesting the potential to search for high-performance TE materials along this direction. This work demonstrates the correlation among high TE performance, NFL quantum criticality, and magnetic fluctuation, which opens up directions for future research.