Quantization of the Hall Conductance in a Three-Dimensional Layer

For the occurrence of the quantum Hall effect (QHE) in a two-dimensional (2D) electron system in a magnetic field, the dissipative components of the conductivity tensor have to be zero with the existence of delocalized electron states below the Fermi level [1]. In a single-particle description, the Landau quantization of the electrons leads to the Landau-level structure with localized states in the gaps between the levels resulting in the integer QHE. The gaps in the electronic density of states can also be caused by electron-electron correlations leading to the fractional QHE in systems with weak disorder [1]. The QHE was also observed in strongly anisotropic systems like a superlattice [2] or an organic metal [3 ‐ 5] which have quasi2D character due to the only weak coupling between 2D conducting layers. In these cases there are also gaps in the density of states in high magnetic fields and the Hall conductance Gxy is quantized to Gxy › 2iNe 2 yh as in N independent 2D parallel layers (i is a small integer and N ? 1). In the superlattice a gap occurs when the cyclotron energy ¯ hvc › ¯