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.
@article{arxiv.2002.11595,
title = {Chern number and orbital magnetization in ribbons, polymers, and layered materials},
author = {Enrico Drigo and Raffaele Resta},
journal= {arXiv preprint arXiv:2002.11595},
year = {2020}
}