  The modern theory of orbital magnetization addresses crystalline materials at
the noninteracting level: therein the observable is the k-space integral of a
geometrical integrand. Alternatively, magnetization admits a local
representation in r space, i.e. a "density" which may address noncrystalline
and/or inhomogeneous materials as well; the Chern number admits an analogous
density. Here we provide the formulation for ribbons, polymers, and layered
materials, where both k-space and r-space integrations enter the definition of
the two observables.

Mesoscale and Nanoscale Physics;Materials Science