Abstract
A field theory of two-dimensional continuum electrons in a strong magnetic field is formulated based on a magnetic lattice representation that preserves translational invariance. The gauge invariance, which is described by the Ward-Takahashi identity, leads to the topologically invariant expression of the Hall conductance and to the exact low-energy theorem. Electrons are localized around a short-range impurity potential and a plateau of the Hall conductance with an integer multiple of ${\mathit{e}}^{2}$/h is realized in the localized state regions. In the presence of extended states at the Fermi energy, ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{y}}$ differs from the quantized value by an amount proportional to the transverse conductance ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{x}}$.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
