Research PapersNo Access

Topological invariance of the Hall conductance and quantization

Paul Bracken

Department of Mathematics, University of Texas, Edinburg, TX 78540-2999, USA

https://doi.org/10.1142/S0217984915501353Cited by:0 (Source: Crossref)

Abstract

It is shown that the Kubo equation for the Hall conductance can be expressed as an integral which implies quantization of the Hall conductance. The integral can be interpreted as the first Chern class of a $U (1)$ principal fiber bundle on a two-dimensional torus. This accounts for the conductance given as an integer multiple of $e^{2} ∕ h$ . The formalism can be extended to deduce the fractional conductivity as well.

Keywords:

PACS: 73.43.-f, 02.30.Jr

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