Magnetic field effects on non-periodic superlattice structures

TL;DR

This paper introduces a numerical transfer matrix method within the effective mass approximation to analyze how magnetic fields influence the energy spectra of non-periodic superlattices, including Fibonacci structures, highlighting orientation-dependent effects.

Contribution

It presents a novel numerical approach for studying magnetic effects on non-periodic superlattices, including quasi-periodic Fibonacci structures, with analysis of magnetic field orientation impacts.

Findings

Perturbations are negligible for B//z but significant for B⊥z.

Energy levels in Fibonacci superlattices become dispersive under perpendicular magnetic fields.

Method effectively captures magnetic field effects in complex superlattice structures.

Abstract

A simple numerical method to study the effect of an applied magnetic field on the energy spectrum of non-periodic superlattice structures is presented. The magnetic field could be either parallel or perpendicular to the growth direction. Our method is based on the transfer matrix technique and on the effective mass approximation. We discuss the advantages and disadvantages of the proposed approach using several examples. In particular, we study the perturbation to the energy spectrum of periodic superlattice induced by the introduction of an enlarged well. We found that these perturbations are negligible for B//z but relevant for B$\perp $z. Preliminary results for Fibonacci superlattices in magnetic fields are presented as well. In these quasi-periodic structures the energy levels become strongly dispersive in presence of a perpendicular magnetic field.