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.
@article{arxiv.0810.1757,
title = {Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials},
author = {F. J. Burnell and B. Andrei Bernevig and D. P. Arovas},
journal= {arXiv preprint arXiv:0810.1757},
year = {2011}
}