Chern Insulator

Quantum anomalous Hall effect without Landau levels — integer Chern number from Berry phase topology of Bloch bands

Mass M (topology) 0.5

Hopping t 1.0

Chern band select C=+1

Edge states speed 1.0

H(k) = d(k)·σ with d(k) = (sin kx, sin ky, M+cos kx+cos ky). Chern number C = (1/4π)∫ d̂·(∂d̂/∂kx × ∂d̂/∂ky). Phase transitions at M=0, ±2t, ±4t. Each domain wall hosts |C| chiral edge modes.