Localization and Metal-Insulator Transition in Multi-Layer Quantum Hall Structures

TL;DR

This paper investigates the phase transitions and Hall conductance behavior in multi-layer quantum Hall systems, revealing how interlayer coupling influences metallic and insulating phases and the quantization of Hall conductance.

Contribution

It introduces an effective field theory and two-loop renormalization group analysis to describe phase structure and conductance quantization in multi-layer quantum Hall systems.

Findings

Finite interlayer tunneling induces successive metallic and insulating phases.

Hall conductivity remains unrenormalized in metallic phases in 3D regime.

Hall conductance is quantized in insulating phases.

Abstract

We study the phase structure and Hall conductance quantization in weakly coupled multi-layer electron systems in the integer quantum Hall regime. We derive an effective field theory and perform a two-loop renormalization group calculation. It is shown that (i) finite interlayer tunnelings (however small) give rise to successive metallic and insulating phases and metal-insulator transitions in the unitary universality class. (ii) The Hall conductivity is not renormalized in the metallic phases in the 3D regime. (iii) The Hall conductances are quantized in the insulating phases. In the bulk quantum Hall phases, the effective field theory describes the transport on the surface.