Pumping current of a Luttinger liquid with finite length

Abstract

We study transport properties in a Tomonaga-Luttinger liquid in the presence of two timedependent point like weak impurities, taking into account finite-length effects. By employing analytical methods and performing a perturbation theory, we compute the backscattering pumping current (I bs) in different regimes which can be established in relation to the oscillatory frequency of the impurities and to the frequency related to the length and the renormalized velocity (by the electron-electron interactions) of the charge density modes. We investigate the role played by the spatial position of the impurity potentials. We also show how the previous infinite length results for I bs are modified by the finite size of the system. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012.