Chern number C = —
Haldane model: H(k) = d(k)·σ, where d(k) = (sin kx, sin ky, M + cos kx + cos ky).
The Berry curvature Ω(k) = ∂kxAy − ∂kyAx (A = Berry connection) acts like a magnetic field in k-space.
The Chern number C = (1/2π)∬Ω d²k ∈ ℤ is a topological invariant — it counts the number of chiral edge modes and cannot change without closing the band gap. Phase transitions occur at M = 0, ±2.
The Berry curvature Ω(k) = ∂kxAy − ∂kyAx (A = Berry connection) acts like a magnetic field in k-space.
The Chern number C = (1/2π)∬Ω d²k ∈ ℤ is a topological invariant — it counts the number of chiral edge modes and cannot change without closing the band gap. Phase transitions occur at M = 0, ±2.