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Chern number (Equation presented) is an integer of Berry curvature (Equation presented) over the whole Brillouin zone and can be expressed explicitly as [7] C= 12π n ∫BZd2k Ωn. The above summation is over all occupied bands below the bulk gap, Ωn(k)=- n′≠n 2 Im((ψnk|vx|ψn′k)(ψn′k|vy|ψnk))(ωn′-ωn)2. Note this summation is over all bands except itself. (Equation presented). Velocity operator (Equation presented). The valley Chern numbers (Equation presented) and (Equation presented) are obtained by integrating the Berry curvature around two valleys (Equation presented) and (Equation presented), respectively
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