Simultaneous quantization of edge and bulk Hall conductivity

Abstract

The edge Hall conductivity is shown to be an integer multiple of $e^2/h$\nwhich is almost surely independent of the choice of the disordered\nconfiguration. Its equality to the bulk Hall conductivity given by the\nKubo-Chern formula follows from K-theoretic arguments. This leads to\nquantization of the Hall conductance for any redistribution of the current in\nthe sample. It is argued that in experiments at most a few percent of the total\ncurrent can be carried by edge states.\n