2003/09/06 by K. Ishikawa, T. Aoyama, Takuya Aoyama +3 · 1 citation
Engineering · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1142/s0217979203023112
published as Int.J.Mod.Phys. B17 (2003) 4765-4818 · 38 pages, 32 figures (one not included), review article
arxiv created 2003/09/06 · openalex publication_date 2003/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the Hall conductance is derived and is used for the proof of the integer quantum Hall effect in the realistic situation. Anisotropic quantum Hall gas is investigated based on the Hartree–Fock approximation in the same formalism. Thermodynamic properties, transport properties, and unusual response under external modulations are found. Implications for the integer quantum Hall effect in the finite systems are also studied and a new quantum Hall regime with non-zero longitudinal resistance is shown to exist.