The geometrical intrinsic contribution to the anomalous Hall conductivity (AHC) of a metal is commonly expressed as a reciprocal-space integral: as such, it only addresses unbounded and macroscopically homogeneous samples. Here we show that the geometrical AHC has an equivalent expression as a local property. We define a "geometrical marker" which actually probes the AHC in inhomogeneous systems (e.g. heterojunctions), as well as in bounded samples. The marker may even include extrinsic contributions of geometrical nature.
@article{arxiv.1702.08885,
title = {Locality of the anomalous Hall conductivity},
author = {Antimo Marrazzo and Raffaele Resta},
journal= {arXiv preprint arXiv:1702.08885},
year = {2017}
}