Scaling of the conductance in a quantum wire

TL;DR

This paper investigates how the electrical conductance of an interacting nano-wire with an impurity scales under different contact conditions using a functional renormalization group approach, revealing distinct behaviors for smooth versus abrupt contacts.

Contribution

It provides a detailed analysis of conductance scaling in quantum wires with impurities, including effects of contact abruptness, using microscopic lattice models and compares with analytical and numerical results.

Findings

One-parameter scaling holds for smooth contacts.

Power-law suppression of conductance occurs with abrupt contacts.

Results agree with analytical and numerical benchmarks.

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.