Microscopic characteristics and tomography scheme of the local Chern marker

The concept of the local Chern marker has gained much attention, especially in the field of ultracold quantum gases in optical lattices and artificial gauge fields. We investigate in further detail the microscopic real-space characteristics of the local Chern marker for the two-band Harper-Hofstadter-Hatsugai model and propose a tomographic scheme for the experimental detection of an approximate local Chern marker neglecting higher orders.