  The notion of charge deficiency from Avron, Seiler, Simon (Charge deficiency,
charge transport and comparison of dimensions, Comm. Math. Phys. 159) is
studied from the view of $KK$-theory and is applied to the Landau levels in
$\C^n$. We calculate the charge deficiencies of the higher Landau levels in
$\C^n$ by means of an Atiyah-Singer type index theorem.
