A many-body marker for three-dimensional topological insulators with inversion symmetry

We extend the previously defined many-body marker for two-dimensional Z₂ topological insulators [I. Gilardoni { et al.}, Phys. Rev. B { 106}, L161106 (2022)] to distinguish trivial, weak-, and strong-topological insulators in three dimensions, in presence of the inversion symmetry. The marker is written in term of ground-state expectation values of position operators and can be employed to detect topological phases of interacting systems beyond mean-field approximations, e.g., within quantum Monte Carlo techniques. Here, we show that the correct results of the non-interacting limit are reproduced by the many-body marker.