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

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.

5 pages, 6 figures

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Cited by in corpus (9)

• Mesoscopic behavior of the transmission phase through confined correlated electronic systems
• Coulomb blockade without potential barriers
• Detection of interaction-induced nonlocal effects using perfectly transmitting nanostructures
• Conductance of nano-systems with interactions coupled via conduction electrons: Effect of indirect exchange interactions
• Effect of flux-dependent Friedel oscillations upon the effective transmission of an interacting nano-system
• Effect of measurement probes upon the conductance of an interacting nanosystem: Detection of an attached ring by non local many body effects
• The embedding method beyond the single-channel case: Two-mode and Hubbard chains
• Transport through two interacting resonant levels connected by a Fermi sea
• Universal Scaling of the Quantum Conductance of an Inversion-Symmetric Interacting Model