Introduction to the theory of the integer quantum Hall effect

作者：Benoît Douçot · 发表于：Comptes Rendus Physique · 年份：2011 · DOI：10.1016/j.crhy.2011.02.003 · 被引用次数：126 · 研究领域：Quantum and electron transport phenomena、Graphene research and applications、Topological Materials and Phenomena

We review the various theoretical arguments which strongly suggest that integer quantization of the Hall conductance holds exactly for a non-relativistic two-dimensional electron system in the presence of a static disorder and electron–electron interactions, when the chemical potential lies in a mobility gap of the system. The semi-classical picture, the Laughlin gauge-invariance argument and the connection between the Kubo Hall conductance and Chern numbers are presented, and the relevance of these idealized geometries to real systems is discussed.