Magnetization direction-controlled topological band structure in TlTiX (X = Si, Ge) monolayers

The quantum anomalous Hall (QAH) insulator is a vital material for the investigation of emerging topological quantum effects, but its extremely low working temperature limits experiments. Apart from the temperature challenge, effective regulation of the topological state of QAH insulators is another crucial concern. Here, by first-principles calculations, we find a family of stable two-dimensional materials TlTiX (X = Si, Ge) are large-gap QAH insulators. Their extremely robust ferromagnetic (FM) ground states are determined by both the direct- and super-exchange FM coupling. In the absence of spin-orbit coupling (SOC), there exist a spin-polarized crossing point located at each