Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials

TL;DR

This paper explores the theoretical possibility of realizing fractional quantum Hall states in three-dimensional isotropic materials, revealing conditions for their stability and phase transitions.

Contribution

It introduces a model for 3D FQH states in bulk materials, including the staging transition and phase diagram analysis, which are novel insights.

Findings

FQH states can exist in 3D bulk materials at low densities with staging transitions.

A phase diagram showing FQH, Wigner crystal, and transition regions.

Identification of the role of Coulomb interactions and phonon correlations.

Abstract

We investigate the possibility of a strongly correlated Fractional Quantum Hall (FQH) state in bulk three dimensional isotropic (not layered) materials. We find that a FQH state can exist at low densities only if it is accompanied by a staging transition in which the electrons re-organize themselves in layers, perpendicular to the magnetic field, at distances of order the magnetic length apart. The Hartree energy associated to the staging transition is off-set by the correlation Fock energy of the 3D FQH state. We obtain the phase diagram of bulk electrons in a magnetic field subject to Coulomb interactions as a function of carrier density and lattice constant. At very low densities, the 3D FQH state exhibits a transition to a 3D Wigner crystal state stabilized by phonon correlations.