THEORETICAL INVESTIGAYTION OF QUANTUM HALL EFFECT

点击翻译按钮获取中文摘要

Various problems of Quantum Hall effect are studied based on field theory that is formulated using von Neumann lattice representation and the following new results have been obtained.1. Integer Quantum Hall effectInteger quantum Hall effect is used for standard of resistance and for determining the fine strusture constant. Concerning finite size effect and finite current effect, it was shown in this project that under sufficently strong magnetic field, corrections vanish and the Hall conductance is quantized exactly in realistic two-dimensional systems. The quantum Hall effect disappears, however, if thhe current exceeds a critical value. The critical Hall field is proportional to two halvth of the magnetic field.2. Fractional Hall effectA new mean field theory of the fractional Hall effect based on flux condenced state on von Neumann lattice is proposed. In this theory, one particle spectrum has a fractal structure owing to two scales of the system, lattice constant and flux per plaquette. The latter is connected with the filling factor. It is shown, for the first time, that the fractional Hall effect is understood from Hofstadter butterfly.3. Periodic potentials in the strong magnetic field and dualityOne particle spectra of the systems with periodic short range potentials are obtained by using von Neumann lattice representation. A kind of duality relation is shown to be hold.4. A symmetry breaking of topological field theory by Gribov copies is analyzed.