High-Chern-Number and High-Temperature Quantum Hall Effect without Landau Levels

The quantum Hall effect (QHE) with quantized Hall resistance of h/{\nu}e2 starts the research on topological quantum states and lays the foundation of topology in physics. Afterwards, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C|=1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C>1). Here, we report the experimental discovery of high-Chern-number QHE (C=2) without Landau levels and C=1 Chern insulator state displaying nearly quantized Hall resistance plateau above the N\'eel temperature in MnBi2Te4 devices. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures.