Eur. Phys. J. B (2012) 85: 136
https://doi.org/10.1140/epjb/e2012-20928-2

Regular Article

Pumping current of a Luttinger liquid with finite length

¹ Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata and IFLP-CONICET, CC 67, 1900 La Plata, Argentina
² Dipartimento di Fisica, Università di Roma “La Sapienza” and INFN, Sezione di Roma1, Piazzale Aldo Moro 2, 00185 Roma, Italy

^a e-mail: salvay@fisica.unlp.edu.ar

Received: 14 November 2011
Received in final form: 23 February 2012
Published online: 26 April 2012

Abstract

We study transport properties in a Tomonaga-Luttinger liquid in the presence of two time-dependent 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.