Impurity and correlation effects on transport in one-dimensional quantum wires

TL;DR

This paper investigates how impurities and electron correlations affect electrical conductance in one-dimensional quantum wires, revealing power-law behaviors and resonant tunneling phenomena across different impurity strengths and temperature regimes.

Contribution

It provides a comprehensive analysis of impurity and correlation effects on transport in quantum wires using the functional renormalization group, including crossover behaviors and resonant tunneling.

Findings

Power-law temperature dependence for single impurities.

Complete crossover from weak to strong impurity regimes.

Universal and non-universal conductance behaviors in double-barrier setups.

Abstract

We study transport through a one-dimensional quantum wire of correlated fermions connected to semi-infinite leads. The wire contains either a single impurity or two barriers, the latter allowing for resonant tunneling. In the leads the fermions are assumed to be non-interacting. The wire is described by a microscopic lattice model. Using the functional renormalization group we calculate the linear conductance for wires of mesoscopic length and for all relevant temperature scales. For a single impurity, either strong or weak, we find power-law behavior as a function of temperature. In addition, we can describe the complete crossover from the weak- to the strong-impurity limit. For two barriers, depending on the parameters of the enclosed quantum dot, we find temperature regimes in which the conductance follows power-laws with "universal" exponents as well as non-universal behavior. Our approach leads to a comprehensive picture of resonant tunneling. We compare our results with those of alternative approaches.