Scenario for fractional quantum Hall effect in bulk isotropic materials

We investigate the possibility of a strongly correlated fractional quantum Hall (FQH) state in bulk three-dimensional (3D) 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 reorganize themselves in layers, perpendicular to the magnetic field, at distances of the order of 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.