Quantum Hall effect in three-dimensional layered systems

Using a mapping of a layered three-dimensional system with significant interlayer tunneling onto a spin Hamiltonian, the phase diagram in the strong magnetic-field limit is obtained in the semiclassical approximation. This phase diagram, which exhibits a metallic phase for a finite range of energies and magnetic fields, and the calculated associated critical exponent $\nu =4/3\mathrm{}$ agree excellently with existing numerical calculations. The implication of this work for the quantum Hall effect in three dimensions is discussed.