Quantum Dots in a Strong Magnetic Field. Quasi-classical Consideration

TL;DR

This paper develops a semi-classical approximation for electron behavior in strong magnetic fields, capturing both classical drift and quantum effects, and demonstrates its effectiveness with simple quantum dot examples.

Contribution

It introduces a novel adiabatic approximation method for analyzing electron dynamics in high magnetic fields, bridging classical and quantum descriptions.

Findings

The approximation accurately describes electron spectra in quantum dots.

It captures collective phenomena in strongly magnetized electron systems.

The method simplifies complex quantum calculations in high magnetic fields.

Abstract

The electron motion in rather strong magnetic fields (when only the lowest Landau level is populated) is considered. In this case the electron kinetic energy is frozen out and the electrons are guided by slowly varied potential. Using the adiabatic procedure and expansion in magnetic length series the approximate description is developed. In zero order this approximation leads to the classical equations of motion describing the Larmor circle drift in the potential gradient. In the second order the special quantum mechanical description where the electron potential energy plays the role of the total Hamiltonian is constructed. Simple examples of a single and two electrons in the parabolic dot demonstrates that the proposed approximate description gives the main features of the electron system spectrum and the collective phenomena.