Thouless Pump

Adiabatic charge pumping — one quantum of charge per cycle, protected by topology




Q = 0.00pumped charge

SSH Pump Cycle (parameter space)

Band Structure E(k) at current phase φ

Charge Density ρ(x,t)

Pumped Charge Q(t)

Thouless (1983) showed that adiabatic charge transport in a periodic potential is quantized: Q = e·C₁, where C₁ is the first Chern number of the occupied band bundle over the (k,φ) torus. This is a topological invariant — it cannot change without closing the band gap. The SSH-like pump modulates hopping amplitudes as t₁=1+δcos(φ), t₂=1-δcos(φ), with on-site potential V=δsin(φ). One full cycle φ: 0→2π pumps exactly one electron regardless of the path (as long as gap stays open).