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

• Published in: The European physical journal. B, Condensed matter physics Vol. 48; no. 2; pp. 243 - 247
• Main Authors: MOLINA, R. A, WEINMANN, D, PICHARD, J.-L
• Format: Journal Article
• Language: English
• Published: Les Ulis Springer 01.11.2005; Berlin EDP sciences; Springer-Verlag
• Subjects: Condensed Matter; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electronic transport in condensed matter; Exact sciences and technology; Mesoscopic Systems and Quantum Hall Effect; Physics; Strongly Correlated Electrons; Theory of electronic transport; scattering mechanisms; Luttinger liquid; Fermion systems; Kondo effect; Charge carrier interaction; Mott insulating; Transport processes; Power law; Quantum transport; mesoscopic transport; electronic correlations
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2005-00403-1

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.