Many-body effects in transport through open systems: pinning of resonant levels

TL;DR

This paper investigates how electron-electron interactions cause resonant energy levels in open quantum dots to pin to the Fermi energy, leading to nonlinear transport behavior and broadening of conduction oscillations, especially under magnetic fields.

Contribution

It demonstrates the nonlinear pinning of resonant levels due to screening effects, contrasting with the traditional linear sweep picture, and examines the impact of magnetic fields on this phenomenon.

Findings

Resonant levels tend to pin to the Fermi energy due to screening.

Pinning causes broadening of conduction oscillations.

Magnetic fields enhance the pinning effect.

Abstract

The role of electron-electron interaction in transport properties of open quantum dots is studied. The self-consistent full quantum mechanical magnetotransport calculations within the Hartree, Density Functional Theory and Thomas-Fermi approximations were performed where a whole device, including the semi-infinitive leads, is treated on the same footing (i.e. the electron-electron interaction is accounted for both in the leads as well as in the dot region). The main finding of the present paper is the effect of pinning of the resonant levels to the Fermi energy due to the enhanced screening. Our results represent a significant departure from a conventional picture where a variation of external parameters (such as a gate voltage, magnetic field, etc.) causes the successive dot states to sweep past the Fermi level in a linear fashion. We instead demonstrate highly nonlinear behavior of the resonant levels in the vicinity of the Fermi energy. The pinning of the resonant levels in open quantum dots leads to the broadening of the conduction oscillations in comparison to the one electron picture. The effect of pinning becomes much more pronounced in the presence of the perpendicular magnetic field. This can be attributed to the enhanced screening efficiency because of the increased localization of the wave function. The strong pinning of the resonant energy levels in the presence of magnetic field can have a profound effect on transport properties of various devices operating in the edge state transport regime. We also critically examine an approximation often used in transport calculations where an inherently open system is replaced by a corresponding closed one.