Haldane model on honeycomb lattice. Compute Berry curvature in k-space and visualize topological edge states. Chern number C=±1 predicts chiral edge modes protected by topology.
Haldane (1988): H(k) = d(k)·σ, d(k) = (Re Σe^{ik·a_i}, Im Σe^{ik·a_i}, M+2t₂cosφ Σcos(k·b_i)). Chern number C = (1/2π)∬ Ω(k)dk, where Ω = ∇_k × A (Berry curvature). Topological phase: |M/t₂cosφ| < 3√3 → C=±1. Bulk-edge correspondence: C chiral edge modes per edge. This was the first theoretical model of a topological Chern insulator.