Thouless Pump

Quantized adiabatic charge transport — one electron per cycle

Charge pumped: 0 e
The Thouless pump adiabatically modulates a periodic potential, transporting exactly one electron per cycle — a consequence of the quantized Berry phase (Chern number C=1) of the filled Bloch band. The pumped charge Q = e·C is a topological invariant, immune to smooth perturbations. This underpins modern topological charge pumps and quantized current standards.