Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials

Details Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials

2008-10-10

arxiv.org/abs/0810.1757v1

Phys. Rev. B 79, 155310 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

10.1103/PhysRevB.79.155310

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.

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