Pumping through a Luttinger liquid ring threaded by a time-varying magnetic field

Abstract

We consider a quantum ring laterally connected to open one-dimensional leads described within the Luttinger liquid (LL) model and subject to a time-dependent driving magnetic field p(t). The closed loop is obtained by connecting two points of the LL by a weak link, which is treated exactly to lowest order in perturbation theory. Analytical results for the current across the weak link, as well as in the external circuit and inside the loop, are obtained. We pay special attention to the case of smooth magnetic pulses such that the response of the system is approximately adiabatic. We find that the response to the flux p is linear only if p is a small fraction of a flux quantum p0. By inserting whole quanta, a current goes in the external wires as two bunches, separated by a time proportional to the length of the loop, and a net pumped current in the external wires is produced. This kind of pumping is consistent with the predictions of the corresponding tight-binding model in the uncorrelated limit, but is not destroyed by electron-electron interactions. © 2013 American Physical Society.