Interacting electron systems between Fermi leads: effective one-body transmissions and correlation clouds

TL;DR

This paper extends the Landauer approach to correlated fermions by modeling how interactions within a scatterer influence conductance through effective one-body transmission, considering the role of leads and correlations.

Contribution

It introduces a method to map many-body scatterers onto effective one-body systems that incorporate lead-induced correlations, revealing how interactions affect conductance.

Findings

Effective transmission deviates by A/L_C from ideal series behavior.

Maximum deviation occurs near the Mott insulator transition.

Conductance depends on lead properties due to electron interactions.

Abstract

In order to extend the Landauer formulation of quantum transport to correlated fermions, we consider a spinless system in which charge carriers interact, connected to two reservoirs by non-interacting one-dimensional leads. We show that the mapping of the embedded many-body scatterer onto an effective one-body scatterer with interaction-dependent parameters requires to include parts of the attached leads where the interacting region induces power law correlations. Physically, this gives a dependence of the conductance of a mesoscopic scatterer upon the nature of the used leads which is due to electron interactions inside the scatterer. To show this, we consider two identical correlated systems connected by a non-interacting lead of length $L\_\mathrm{C}$. We demonstrate that the effective one-body transmission of the ensemble deviates by an amount $A/L\_\mathrm{C}$ from the behavior obtained assuming an effective one-body description for each element and the combination law of scatterers in series. $A$ is maximum for the interaction strength $U$ around which the Luttinger liquid becomes a Mott insulator in the used model, and vanishes when $U \to 0$ and $U \to \infty$. Analogies with the Kondo problem are pointed out.