Adiabatic transport in nanostructures

A confined system of noninteracting electrons, subject to the combined effect of a time-dependent potential and different external chemical potentials, is considered. The current flowing through such a system is obtained by using the adiabatic approximation in an iterative manner. A formula is derived for the charge pumped through an unbiased system (all external chemical potentials are kept at the same value); it reproduces the Brouwer formula for a two-terminal nanostructure. The formalism presented yields the effect of the chemical-potential bias on the pumped charge on one hand, and the modification of the Landauer formula (which gives the current in response to a constant chemical-potential difference) brought about by the modulating potential on the other. Corrections to the adiabatic approximation are derived and discussed.