Quantized adiabatic charge transport — exactly 1 charge per cycle (topological)
θ = 0 | Charge pumped: 0.00
The Thouless pump: a 1D tight-binding chain H(θ) = Σ[t + δcos(θ)]c†ᵢcᵢ₊₁ + Σ[Δ·sin(θ)]nᵢ
with parameter θ cycling 0 → 2π. The center of mass of the filled band shifts by exactly 1 lattice site
per cycle — a topological invariant equal to the Chern number C=1. No matter how slowly (adiabatically)
you vary θ, exactly one quantum of charge is transported. Top: band structure vs θ. Bottom: charge transport tracker.
The quantization is protected by the bulk gap — it cannot be changed by smooth deformations.