The Berry curvature per solid angle is given by Ω Ω ¯ ¯ θ θ ϕ ϕ = Ω Ω θ θ ϕ ϕ / sin ⁡ ⁡ θ θ = 1 / 2 . In this case, the Berry phase corresponding to any given path on the unit sphere S 2 in magnetic-field space is just half the solid angle subtended by the path. The integral of the Berry curvature over the whole sphere is therefore exactly 2 π π , so that the Chern number is unity, consistent with the Chern theorem.