THEORETICAL INVESTIGAYTION OF QUANTUM HALL EFFECT
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
|Research Institution||HOKKAIDO UNIVERSITY|
ISHIKAWA Kenzo Hokkaido Univ.Grad.School of Sci.Prof., 大学院・理学研究科, 教授 (90159690)
|Project Period (FY)
1995 – 1996
Completed(Fiscal Year 1996)
|Budget Amount *help
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1996 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1995 : ¥1,100,000 (Direct Cost : ¥1,100,000)
|Keywords||Quantum Hall effect / fractional Hall effect / von Neumann lattice / flux phase / Hofstadter butterfly / duality / topological field theory / quantum field theory / von Neumann格子表現 / 有限サイズ補正 / 抵抗標準|
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 effect
Integer 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 effect
A 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 duality
One 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.
Research Products (19results)