Quantum Hall Effect in Three Dimensional Layered Systems

TL;DR

This paper maps a layered 3D system with inter-layer tunneling onto a spin-Hamiltonian to analyze the quantum Hall effect, revealing a metallic phase and critical behavior consistent with numerical results.

Contribution

It introduces a semi-classical approach to derive the phase diagram of 3D layered systems exhibiting quantum Hall effect, highlighting a metallic phase and critical exponent.

Findings

Existence of a metallic phase in the phase diagram.

Critical exponent $ u=4/3$ matches numerical calculations.

Implications for 3D quantum Hall effect discussed.

Abstract

Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram, which exhibit a metallic phase for a finite range of energies and magnetic fields, and the calculated associated critical exponent, $\nu=4/3$, agree excellently with existing numerical calculations. The implication of this work for the quantum Hall effect in three dimensions is discussed.