Landau quantization of Dirac fermions in graphene and its multilayers

When electrons are confined in a two-dimensional （2D） system, typical quantum-mechanical phenonl- ena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum-mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behav- iors of Dirac fernlions in monolayer and multilayer graphene by using scanning tunneling microscopy （STM） and scanning tulmeling spectroscopy （STS）. Through STS measurement of the strong mag- netic fields, distinct Landau-level spectra and rich level-splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fllndamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties.