Quantum pump effect in one-dimensional systems of Dirac fermions

We investigate the behavior of the directed current in one-dimensional systems of Dirac fermions driven by local periodic potentials in the forward as well as in backscattering channels. We treat the problem with Keldysh nonequilibrium Green's function formalism. We present the exact solution for the case of an infinite wire and show that in this case the dc current vanishes identically. We also investigate a confined system consistent in an annular arrangement coupled to a particle reservoir. We present a perturbative treatment that allows for the analytical expressions of the dc current in the lowest order of the amplitudes of the potential. We also present results obtained from the numerical solution of the exact Dyson's equations.