Observation of a Chern insulator in crystalline ABCA-tetralayer graphene with spin-orbit coupling

Degeneracies in multilayer graphene, including spin, valley, and layer degrees of freedom, can be lifted by Coulomb interactions, resulting in rich broken-symmetry states. Here, we report a ferromagnetic state in charge-neutral ABCA-tetralayer graphene driven by proximity-induced spin-orbit coupling from adjacent tungsten diselenide. The ferromagnetic state is identified as a Chern insulator with a Chern number of 4; its maximum Hall resistance reaches 78% quantization at zero magnetic field and is fully quantized at either 0.4 or –1.5 tesla. Three distinct broken-symmetry insulating states, layer-antiferromagnet, Chern insulator, and layer-polarized insulator, along with their transitions, can be continuously tuned by the vertical displacement field. In this system, the magnetic order of the Chern insulator can be switched by three knobs, including magnetic field, electrical doping, and vertical displacement field.

Methods
Transport measurements above 1.5 K were performed in an Oxford variable temperature insert (VTI) system. Measurements at 0.1 K were performed in a Leiden dilution refrigerator. Stanford Research Systems. SR860, SR830, and Guangzhou Sine Scientific Instrument OE1201 lock-in amplifiers were used to measure the sample resistances with a small ac bias current of 1~10 nA at a low frequency (~17.7 Hz). 

Data processing and plotting are mainly carried out in the Origin.