Quantum and semiclassical study of magnetic anti-dots

TL;DR

This paper investigates the energy levels and current flow patterns of charged particles in magnetic anti-dots, using semiclassical and quantum methods, revealing good agreement and classifying orbit types.

Contribution

It provides a detailed semiclassical analysis of magnetic anti-dots and compares it with exact quantum calculations, offering new insights into their spectral properties.

Findings

Good agreement between semiclassical and quantum spectra in weak magnetic fields

Classification of energy spectra into six orbit classes

Clear correspondence between quantum states and classical trajectories

Abstract

We study the energy level structure of two-dimensional charged particles in inhomogeneous magnetic fields. In particular, for magnetic anti-dots the magnetic field is zero inside the dot and constant outside. Such a device can be fabricated with present-day technology. We present detailed semiclassical studies of such magnetic anti-dot systems and provide a comparison with exact quantum calculations. In the semiclassical approach we apply the Berry-Tabor formula for the density of states and the Borh-Sommerfeld quantization rules. In both cases we found good agreement with the exact spectrum in the weak magnetic field limit. The energy spectrum for a given missing flux quantum is classified in six possible classes of orbits and summarized in a so-called phase diagram. We also investigate the current flow patterns of different quantum states and show the clear correspondence with classical trajectories.