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Extensive investigations on topological phase transition (TPT) inthree-dimensional compounds have been done. whereas, rare in two-dimensionalsystems, let alone noncentrosymmetric materials. In this work, based onfirst-principles calculations, we explore an inversion symmetry brokenstructural ReC2H monolayer. We reveal that it undergoes two TPTs, namely fromnormal insulator to Z2 topological insulator and back to normal insulator, atthe critical biaxial strain of 2.3% and 7.8%, respectively. The band inversionoccurs at the generic momentum in the first TPT, while at high symmetric Kpoint in the second one. Usually, band inversion is identified by the exchangein the components or irreducible representations of the wavefunctions. Thesequantities can be easily obtained in theoretical calculation but hard to bedetected in experimental techniques like Angle-resolved photoemissionspectroscopy. It is well known that nonlinear optical (NLO) response is verysensitive to the components and symmetries of the engaged bands, which alsoincorporates information of band topology. Therefore, we study the shiftcurrent, one of the widely explored NLO responses in noncentrosymmetricsystems, during the two TPTs. We find that in both cases band inversion leadsto the sign change of shift vectors around the momenta where the bandgap closesand reopens. Whereas the shift current, as the overall contribution of shiftvectors weighted by the absorption rate in the whole Brillouin zone, may keepits direction. This work offers insight that a scrutinized examination ishighly demanded in utilizing shift current to detect TPT.

Switchable Topological Phase Transition and Novel Nonlinear Optical Properties in ReC2H Monolayer