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The TiSiCO-family monolayer $X_2Y$CO$_2$($X$=Ti, Zr, Hf; $Y$=Si, Ge) is atwo-dimensional second-order topological insulator with unique valley-layercoupling in equilibrium condition. In this work, based on the four-bandtight-binding (TB) model of monolayer Ti$_2$SiCO$_2$ (ML-TiSiCO) and theFloquet theory, we study the non-equilibrium properties of the ML-TiSiCO undera periodic field of laser and a gate-electric field. We find the interactionbetween the time-periodic polarized light and the electric field can lead to avariety of intriguing topological phase transitions. By driving the system withonly circularly polarized light (CPL), a photoinduced topological phasetransition occurs from a second-order topological insulator to a Cherninsulator with a Chern number of $C=\pm$2, and the sign of the Chern number $C$is determined by the chirality of the incident light. Further adding aperpendicular electric field, we find that the ML-TiSiCO exhibits a rich phasediagram, consisting of Chern insulators with different Chern numbers andvarious topological semimetals. In contrast, since the linearly polarized light(LPL) does not break time-reversal symmetry, the Chern number of the systemwould not be changed under the irradiation of LPL. However, there still existmany topological phases, including second-order topological insulator,topological semi-Dirac, Dirac and valley-polarized Dirac semimetals under theinteraction between the LPL and the electric field. Our results not onlyenhance the understanding of the fundamental properties of ML-TiSiCO but alsobroaden the potential applications of such materials in optoelectronic devices.

Photoinduced topological phase transition in monolayer Ti$_2$SiCO$_2$