A scattering matrix approach to quantum pumping: beyond the small-AC-driving-amplitude limit

In the adiabatic and weak-modulation quantum pump, net electron flow is driven from one reservoir to another by absorbing or emitting an energy quantum \hbar\omega from or to the reservoirs. This paper considers high-order dependence of the scattering matrix on the time. Non-sinusoidal behaviour of strong pumping is revealed. The relation between the pumped current and the ac driving amplitude varies from power of 2, 1 to 1/2 when stronger modulation is exerted. Open experimental observation can be interpreted by multi-energy-quantum-related processes.