Three-dimensional oscillator in magnetic field: the de Haas-van Alphen effect in mesoscopic systems

TL;DR

This paper theoretically explores the de Haas-van Alphen oscillations in mesoscopic three-dimensional systems, revealing size-dependent effects and temperature constraints on the observability of these quantum oscillations.

Contribution

It introduces the first theoretical model for dHvA oscillations in 3D mesoscopic systems with detailed size and temperature effects.

Findings

dHvA oscillations are size-dependent and observable within a specific temperature range

lower size limit for observing oscillations is approximately 20 electrons

oscillation period stretches as the system size decreases

Abstract

The theoretical investigation of the cluster de Haas - van Alphen (dHvA) oscillations in three-dimensional systems performed for the first time. Applying a three-dimensional oscillator model to systems with electron numbers $10< N \leq 10^5$ we predict distinctive size effects: the dHvA oscillations can be observed only within a certain temperature range determined by $N$; the lower size limit for $N$ is $\approx 20$; the amount of the dHvA oscillations is reduced with decreasing $N$ which is accompanied by stretching the period of the oscillations.