Notes on Infinite Layer Quantum Hall Systems

Abstract

We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics such as quasiparticles with non-trivial internal structure, irrational braiding phases, and the necessity of a boundary hierarchy construction for interlayer correlated states. The bulk states host a family of surface phases obtained by hybridizing the edge states in each layer. We analyze the surface conduction in these phases by means of sum rule and renormalization group arguments and by explicit computations at weak tunneling in the presence of disorder. We find that in cases where the interlayer electron tunneling is not relevant in the clean limit, the surface phases are chiral semi-metals that conduct only in the presence of disorder or at finite temperature. We show that this class of problems which are naturally formulated as interacting bosonic theories can be fermionized by a general technique that could prove useful in the solution of such ``one and a half'' dimensional problems.

RevTeX, 2 eps figs included, 35p., for a summary see http://xxx.lanl.gov/abs/cond-mat/0006432

References in corpus (6)

• Three-dimensional disordered conductors in a strong magnetic field: surface states and quantum Hall plateaus
• Chiral Surface States in the Bulk Quantum Hall Effect
• Quantum Hall Bilayers and the Chiral Sine-Gordon Equation
• The fractional quantum Hall effect in infinite layer systems
• Interlayer Magnetic Coupling and the Quantum Hall Effect in Multilayer Electron Systems
• Dynamics of the Compact, Ferromagnetic ν=1 Edge

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• Broken-Symmetry States in Quantum Hall Superlattices
• Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials
• Quantum-Hall physics and three dimensions
• Electron Interactions and Transport Between Coupled Quantum Hall Edges
• Transport between edge states in multilayer integer quantum Hall systems: exact treatment of Coulomb interactions and disorder
• Three-dimensional fracton topological orders with boundary Toeplitz braiding
• Floating topological phases
• Bilayers and quasi-3D stacks of Jain series fractional quantum Hall states from parton construction