Universal topological marker

We elaborate that for topological insulators and superconductors described by Dirac models in any dimension symmetry class, the order can be mapped to lattice sites a universal marker. Deriving from recently discovered momentum-space invariant, we introduce operator consists of alternating projectors filled empty eigenstates position operators, multiplied matrices are omitted Hamiltonian. The projected yields marker, whose form is explicitly constructed every topologically nontrivial class 1D 3D. off-diagonal elements nonlocal which decays with correlation length diverges at phase transitions, represents Wannier state function. Various prototype examples, including Su-Schrieffer-Heeger model, Majorana chain, Chern insulators, Bernevig-Hughes-Zhang 2D chiral helical $p$-wave superconductors, model $^{3}$He B-phase, 3D time-reversal symmetric etc, employed demonstrate ubiquity our formalism.