Spontaneous coherence and the quantum Hall Effect in triple-layer electron systems

TL;DR

This paper explores how spontaneous interlayer coherence can lead to the quantum Hall effect in triple-layer electron systems, using a simplified model and advanced approximations to map out the conditions for this phenomenon.

Contribution

It introduces a simple tight-binding model and applies Hartree-Fock methods to analyze phase coherence and quantum Hall states without interlayer tunneling.

Findings

Identification of phase regions with quantum Hall effect

Validation of the model against experimental data

Mapping of the phase diagram for triple-layer systems

Abstract

We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy is verified by comparison with recent experiments. By calculating the ground state in an unrestricted Hartree-Fock approximation and the collective-mode spectrum in a time-dependent Hartree-Fock approximation, we construct a phase diagram delimiting regions in the parameter space of the model where the integer quantum Hall effect occurs in the absence of interlayer tunneling.