Bosonization approach to the edge reconstruction of two dimentional electron systems in a quantum dot

TL;DR

This paper introduces a bosonization method to analyze edge reconstruction in two-dimensional electron systems within quantum dots, revealing how magnetic field strength and electron number influence the phenomenon.

Contribution

It develops a novel bosonization scheme for 2D electron systems to study edge reconstruction under magnetic fields.

Findings

Edge reconstruction occurs at a critical magnetic field value.

Reconstruction depends on the number of electrons.

Third order bosonic terms affect the Hamiltonian.

Abstract

We consider the edge reconstruction of electrons in a two dimensional harmonic trap under a strong magnetic field. In this system the edge reconstruction occurs as a result of competition between electron-electron interaction and confining potential. To describe it, we develop a bosonization scheme for two dimensional electron systems. With this method we obtain the excitation spectrum and demonstrate that the edge reconstruction occurs when the value of the magnetic field reaches a critical value. We also show that the edge reconstruction depends on the number of electrons. Additionally, we calculate the third order terms of bosons in Hamiltonian and examine the effect of those terms with a perturbation theory.