Topological Pump — Rice-Mele Model
Adiabatic cycling pumps exactly one charge per cycle — a topological invariant
H(k,φ) = [t+δt·cos φ]σₓ + [δt·sin φ]σᵧ + [Δ·cos φ]σᵤ | C = 1/(2π) ∮ Ω dk dφ = 1
φ = 0.00π | Pumped charge Q = 0.00
The Rice-Mele model pumps exactly one quantum of charge per adiabatic cycle — a consequence of the
Chern number C=1 of the occupied band bundle in (k,φ) parameter space.
This is the 1D analog of the quantum Hall effect. Left: band structure. Right: accumulated charge vs pump phase.