Change of the Chern number at band crossings

Abstract

Let $H(\epsilon ,x)$ be a finite dimensional hermitian matrix depending on the variable $x$ taking its values on a 2D manifold and changing with $\epsilon$. If at $\epsilon =0$ two bands are touching, we give a formula for the change of Chern number of these bands as $\epsilon$ passes through zero.

arXiv commentuuencoded version, 6 pages latex, 2 postscript figures included

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