Electronic Structure of Three-Dimensional Superlattices Subject to Tilted Magnetic Fields

TL;DR

This paper investigates the electronic structure of 3D superlattices under tilted magnetic fields, comparing quantum-mechanical and quasi-classical approaches, and introduces a new tight-binding model for accurate analysis.

Contribution

It presents a fully-quantum-mechanical tight-binding model for superlattice electrons in tilted magnetic fields, highlighting limitations of the quasi-classical approach.

Findings

Quasi-classical approach fails in certain cases.

Proposed tight-binding quantum model accurately describes electronic structure.

Identifies conditions where quantum effects dominate over classical approximations.

Abstract

Full quantum-mechanical description of electrons moving in 3D structures with unidirectional periodic modulation subject to tilted magnetic fields requires an extensive numerical calculation. To understand magneto-oscillations in such systems it is in many cases sufficient to use the quasi-classical approach, in which the zero-magnetic-field Fermi surface is considered as a magnetic-field-independent rigid body in k-space and periods of oscillations are related to extremal cross-sections of the Fermi surface cut by planes perpendicular to the magnetic-field direction. We point out cases where the quasi-classical treatment fails and propose a simple tight-binding fully-quantum-mechanical model of the superlattice electronic structure.