Theory of Two-Dimensional Electron Systems Under Strong Magnetic Field at Low Temperatures

K. Yamada, T. Uchida, M. Fujita, T. Toyoda
Tokai University, JP

Keywords: graphene 2DES


Research on the 2DES under magnetic fields has developed remarkably for the last decades. In particular, the two experimental discoveries are the most striking: the quantum Hall effect (QHE) by Von Klitzing and the fractional quantum Hall effect (FQHE) by Tsui, Stormer, and Gossard. Although these two tremendous achievements were made experimentally, these phenomena could not be fully explained quantitatively. So far the electron reservoir model has been the only model that can explain the experimental data precisely. Three decades after these discoveries, the QHE was also observed in graphene 2DES. Since the graphene 2DES has the zero-mass Dirac excitations, the discovery of QHE has become one of the most challenging theoretical problems in modern solid state physics. However, no theoretical attempts have succeeded in reproducing the experimental data until the beginning of this year when Toyoda and Zhang published their theory by adopting the electron reservoir hypothesis. In this work we discuss the mechanism of the electron reservoir from a statistical mechanical point of view with its potential application to other phenomena in condensed matter physics.