Physics – Condensed Matter
Scientific paper
1995-07-21
Phys. Rev. B54 (1996) 17819
Physics
Condensed Matter
48 pages, figures not included, some additions and revisions
Scientific paper
10.1103/PhysRevB.54.17819
A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator in the momentum representation, is realized. In QHR, the Hall conductance is given by a topological invariant of the momentum space and is quantized exactly. The edge states do not modify the value and topological property of $\sigma_{xy}$ in QHR. We next compute distribution of current based on effective action and find a finite amount of current in the bulk and the edge, generally. Due to the Hall electric field in the bulk, breakdown of the QHE occurs. The critical electric field of the breakdown is proportional to $B^{3/2}$ and the proportional constant has no dependence on Landau levels in our theory, in agreement with the recent experiments.
Ishikawa Kaoru
Maeda Nobuki
Tadaki Kohtaro
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