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Nonlinear optical responses are often used as a probe for studying electronicproperties of materials. For topological materials, studies so far focused onthe photogalvanic electric current, which requires breaking inversion symmetry.In this work we present a theory of orbital current response ininversion-symmetric topological insulators. We find a symmetry-allowed orbitalcurrent response that occurs in centrosymmetric materials under illumination bylinearly polarized light. The sign of the dc nonlinear conductivity reflectsthe $\mathbb{Z}_2$ index and the conductivity changes sign at the transitionbetween trivial and topological insulator phases. We derive an expression forthe nonlinear orbital photocurrent for a general class of models with twodoubly degenerate bands, and discuss its specific applications in the cases ofthe Bernevig-Hughes-Zhang model and the 1T' phase of transition metaldichalcogenides. Experimental setups for observation of the orbital current arealso discussed.

Nonlinear orbital response across topological phase transition in centrosymmetric materials