Zero modes and the quantized Hall conductance of the two-dimensional lattice in a magnetic field
- 1 June 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 39 (16) , 11943-11949
- https://doi.org/10.1103/physrevb.39.11943
Abstract
Several properties of the tight-binding electrons in two dimensions with a uniform magnetic field perpendicular to the plane are discussed. The existence of zero-energy states is explicitly shown. The quantized value of the Hall conductance of each magnetic subband which is the Chern number of a certain fiber bundle on a two-torus is calculated. The holelike Hall coefficient can be explained by the quantum mechanics of negatively charged electrons.Keywords
This publication has 13 references indexed in Scilit:
- Topological invariant and the quantization of the Hall conductancePublished by Elsevier ,2004
- The resonating valence bond state and high-Tc superconductivity — A mean field theorySolid State Communications, 1987
- Global scaling properties of the spectrum for a quasiperiodic schrödinger equationPhysical Review B, 1986
- Quantised Hall conductance in a perfect crystalJournal of Physics C: Solid State Physics, 1985
- Quantal phase factors accompanying adiabatic changesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1984
- Renormalization-group analysis of the discrete quasiperiodic Schrödinger equationPhysical Review B, 1984
- Metal-Insulator Transition and Scaling for Incommensurate SystemsPhysical Review Letters, 1983
- Homotopy and Quantization in Condensed Matter PhysicsPhysical Review Letters, 1983
- Quantized Hall Conductance in a Two-Dimensional Periodic PotentialPhysical Review Letters, 1982
- Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fieldsPhysical Review B, 1976