Topological Thouless Pump — Rice-Mele
Quantized adiabatic charge transport via Berry phase winding in parameter space
Thouless pump (1983): The Rice-Mele model H = Σ[t(1±δcos φ)·c†_{i+1}c_i + Δsin(φ)·(−1)^i·n_i] has a parameter space (δ, Δ, φ) with a topological invariant — the Chern number C = 1 when the pump cycle encloses the degeneracy point. Per cycle, exactly C electrons are transported: ΔQ = C·e. This is the 1D analogue of the quantum Hall effect, with φ playing the role of k_y. Experimentally realized with cold atoms in optical lattices (Nakajima, Tomita et al. 2016).