Searching for novel two-dimensional (2D) materials is crucial for the development of the next generation technologies such as electronics, optoelectronics, electrochemistry and biomedicine. In this work, we designed a series of 2D materials based on endohedral fullerenes, and revealed that many of them integrate different functions in a single system, such as ferroelectricity with large electric dipole moments, multiple magnetic phases with both strong magnetic anisotropy and high Curie temperature, quantum spin Hall effect or quantum anomalous Hall effect with robust topologically protected edge states. We further proposed a new style topological field-effect transistor. These findings provide a strategy of using fullerenes as building blocks for the synthesis of novel 2D materials which can be easily controlled with a local electric field.
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