Integer quantum Hall effect

Abstract

Integer quantum Hall effect, which is the Hall effect quantized into integer times e2/h (e: elementary charge, h: Planck's constant) observed first in two-dimensional electron gases in strong magnetic fields, is reviewed from both theoretical and experimental standpoints. Basic physics underlying the phenomenon is explained. We also mention diverse advances such as the quantum Hall effect (QHE) in various materials and contexts that include graphene, oxides and narrow-gap semiconductors, a relation with the fractional quantum Hall effect, and the quantum Hall effect as the resistance standard and a furhter role in the new SI system. Specifically, while the quantum Hall effect is historically the first realization of the topological systems, there are vast developments into a much wider realm of physics, so that in this new edition we have a fresh look at QHE in the light of recent physical concepts in topological physics. Thus we expound in particular:•A perspective of topological systems•For the graphene QHE, the twisted bilayer graphene, and•The Floquet topological insulator (a light-matter coupled system) as a new paradigm in nonequilibrium topological systems, where an anomalous quantum Hall effect in zero magnetic field is realized as theoretical predicted to occur in graphene illuminated by a circularly-polarized laser and experimentally veryfied recently.