Thouless Pump — Adiabatic Topological Charge Pumping

Pump Parameters

Pump phase φ/2π: 0.00 Modulation V₁: 1.00 Dimerization δ: 0.50 Animate speed: 1.0

Topological Observables

Pump phase φ: –
Chern number C₁: +1
Pumped charge Q: –
Cycles: 0
Band gap: –

Thouless (1983): adiabatic charge pumped per cycle = Chern number C = ∮ Berry curvature dk dφ / 2π. Exactly quantized as long as gap remains open. SSH-like model: H(k,φ) = [t+δcos(φ)]σ_x + [δsin(φ) + V₁sin(k)]σ_y. Experimentally realized in cold atoms and photonic lattices.