THE EVOLUTION OF THE TOPOLOGICAL-STRUCTURE OF THE INTEGRAL QUANTUM HALL-EFFECT

The topological structure of the integral Hall conductance is determin ed by making use of the decomposition of the gauge potential on a U(1) principal fibre bundle over k-space. The integral Hall conductance de nsity is found to take the form of a delta-function delta(psi). Only t he zeroes of Bloch waves contribute to the Hall conductance. The topol ogical structure of the integral Hall conductance is labeled by the Ho pf index beta and the Brouwer degree eta. The Hall conductance topolog ical current and its evolution is discussed. The Hall topological char ges are found generating or annihilating at the limit points of wave f unction and splitting and merging at the bifurcation points of the wav e function. Different directions of the bifurcation are given. (C) 199 8 Published by Elsevier Science B.V.