Thouless pump (1983): a 1D lattice with periodically modulated hopping/potential adiabatically pumps exactly one charge per cycle.
The pumped charge equals the
Chern number C ∈ ℤ of the occupied band over the (k, φ) torus:
Q = C = (1/2π) ∮ F_{kφ} dk dφ
where F is the Berry curvature. Quantization is topologically protected — small perturbations cannot change an integer.
The Rice-Mele model generalizes the SSH model by adding a staggered on-site potential, creating a pumping cycle.