Multiple Particle Scattering in Quantum Point Contacts

TL;DR

This paper models how enhanced Coulomb interactions in quantum point contacts lead to increased multi-electron scattering, reducing resistance at low bias, with predictions on effective charge measurable via shot noise.

Contribution

It introduces a model using a spinful Tomonaga-Luttinger liquid with an impurity to explain anomalous scattering and conductance behavior in quantum point contacts.

Findings

Enhanced two-electron scattering dominates conductance at strong Coulomb interactions.

Effective charge approaches 2e at high backscattering current.

Model predictions can be tested through shot noise experiments.

Abstract

Recent experiments performed on weakly pinched quantum point contacts, have shown a resistance that tend to decrease at low source drain voltage. We show that enhanced Coulomb interactions, prompt by the presence of the point contact, may lead to anomalously large multiple-particle scattering at finite bias voltage. These processes tend to decrease at low voltage, and thus may account for the observed reduction of the resistance. We concentrate on the case of a normal point contact, and model it by a spinfull interacting Tomonaga-Luttinger liquid, with a single impurity, connected to non interacting leads. We find that sufficiently strong Coulomb interactions enhance two-electron scattering, so as these dominate the conductance. Our calculation shows that the effective charge, probed by the shot noise of such a system, approaches a value proportional to e* = 2e at sufficiently large backscattering current. This distinctive hallmark may be tested experimentally. We discuss possible applications of this model to experiments conducted on Hall bars.