Pumping at resonant transmission and transferred charge quantization

We consider pumping through a small quantum dot separated from the leads by two point contacts, whose conductances, G1 and G2, serve as pumping parameters. When the dot is pinched, i.e., G1,G2 e2/h, we find that there is a “resonance line” in the parameter plane {G1, G2} along which the Fermi energy in the leads aligns with the energy of the quasi-bound state in the quantum dot. When G1 and G2 are modulated periodically and adiabatically such that the pumping contour defined by G1=G1(t) and G2=G2(t) encircles the resonance line, the current is quantized: the charge pumped through the dot during each period of the modulation is close to a single electronic charge.