Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

TL;DR

This paper investigates how the geometry of leads and wire length in a Luttinger liquid affects the temperature-dependent conductance, revealing complex behavior with multiple temperature scales beyond simple power-law predictions.

Contribution

It introduces a detailed analysis of temperature scales in conductance for finite-length Luttinger liquids coupled at arbitrary points, extending understanding beyond end-coupled systems.

Findings

Multiple temperature regimes with distinct power-law behaviors.

Presence of crossover regions disrupting simple scaling.

Geometry significantly influences conductance temperature dependence.

Abstract

We study electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (two-dimensional) leads, thereby bringing theory closer towards systems closer to setups realized in experiments. In particular, we compute the temperature dependence of the linear conductance $G$ of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of overhanging parts of the leads and the wire implies a $G(T)$ which is much more complex than the power-law behavior described so far for end-coupled wires. Depending on the precise setup the wide temperature regime of power-law scaling found in the end-coupled case is broken up in up to five fairly narrow regimes interrupted by extended crossover regions. Our results can be used to optimize the experimental setups designed for a verification of Luttinger liquid power-law scaling.