  Topological invariants are global properties of the ground-state wave
function, typically defined as winding numbers in reciprocal space. Over the
years, a number of topological markers in real space have been introduced,
allowing to map topological order in heterogeneous crystalline and disordered
systems. Notably, even if these formulations can be expressed in terms of
lattice-periodic quantities, they can actually be deployed in open boundary
conditions only, as in practice they require computing the position operator
$\mathbf{r}$ in a form that is ill-defined in periodic boundary conditions.
Here we derive a local Chern marker for infinite two-dimensional systems with
periodic boundary conditions in the large supercell limit, where the electronic
structure is sampled with one single point in reciprocal space. We validate our
approach with tight-binding numerical simulations on the Haldane model,
including trivial/topological superlattices made of pristine and disordered
Chern insulators. The strategy introduced here is very general and could be
applied to other topological invariants and quantum-geometrical quantities in
any dimension.
