Scaling of the conductance in a quantum wire

¹ Institut für Theoretische Physik, Universität Göttingen Tammannstr. 1, D-37077 Göttingen, Germany
² Max-Planck-Institut für Festkörperforschung Heisenbergstr. 1, D-70569 Stuttgart, Germany

Received: 10 March 2003
Accepted: 6 October 2003

Abstract

The conductance G of an interacting nano-wire containing an impurity and coupled to non-interacting semi-infinite leads is studied using a functional renormalization group method. We obtain results for microscopic lattice models without any further idealizations. For an interaction which is turned on smoothly at the contacts we show that one-parameter scaling of G holds. If abrupt contacts are included, we find power law suppression of G with an exponent which is twice as large as the one obtained for smooth contacts and no one-parameter scaling. Our results show excellent agreement with the analytically known scaling function at Luttinger liquid parameter K=1/2 and numerical density matrix renormalization group data.