Symmetry-allowed nonlinear orbital response across the topological phase transition in centrosymmetric materials

Nonlinear optical responses are commonly used as a probe for studying the electronic properties of materials. For topological materials, studies thus far focused on photogalvanic electric currents, which forbidden in centrosymmetric materials because they require broken inversion symmetry. In this Letter, we propose class symmetry-allowed inversion-symmetric insulators with two doubly degenerate bands. We consider specific example such response, orbital current, and show that sign response reflects ${\mathbb{Z}}_{2}$ index, i.e., current changes at transition between trivial insulator phases. This is illustrated models insulators: Bernevig-Hughes-Zhang model $1{T}^{\ensuremath{'}}$ phase metal dichalcogenides.