Quantum Hall Effect: From the Winding Number to the Flow Diagram
To answer a query as to what extent the quantised Hall effect is universal, we show that (i) an exact proof for the quantisation of Hall conductivity is given by the topological invariant (winding number), (ii) there exists a definite distribution of winding numbers as a function of energy for given system size and degree of disorder giving rise to a well-behaved σxy for lattice systems with Landau-level mixing and (iii) the flow diagram for σxy vs σxx obtained by the Thouless number exhibits characteristic behaviours.
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