Interplay of size and Landau quantizations in the de Haas-van Alphen oscillations of metallic nanowires

TL;DR

This paper investigates how size and Landau quantizations influence de Haas-van Alphen oscillations in metallic nanowires, revealing new fundamental frequencies and damped resonances under hard boundary conditions.

Contribution

It provides a detailed analysis of quantum oscillations in nanowires with infinite well boundaries, contrasting with previous soft boundary models, and identifies new oscillation frequencies and resonances.

Findings

Two fundamental frequencies in nanowires differ from bulk systems.

Damped 'magic resonances' similar to previous models are observed.

Analytic and numerical spectra show good agreement.

Abstract

We examine the interplay between size quantization and Landau quantization in the De Haas-Van Alphen oscillations of clean, metallic nanowires in a longitudinal magnetic field for `hard' boundary conditions, i.e. those of an infinite round well, as opposed to the `soft' parabolically confined boundary conditions previously treated in Alexandrov and Kabanov (Phys. Rev. Lett. {\bf 95}, 076601 (2005) (AK)). We find that there exist {\em two} fundamental frequencies as opposed to the one found in bulk systems and the three frequencies found by AK with soft boundary counditions. In addition, we find that the additional `magic resonances' of AK may be also observed in the infinite well case, though they are now damped. We also compare the numerically generated energy spectrum of the infinite well potential with that of our analytic approximation, and compare calculations of the oscillatory portions of the thermodynamic quantities for both models.