Quantum geometry, which is often studied through Berry curvature and quantum metric, has been found to dictate the properties of electrons in highly unusual ways. In this presentation, I will discuss how the interaction between quantum geometry and circularly polarized light can be used to control the material phase. I will provide two examples to illustrate this phenomenon. The first example is the realization of the optical chiral induction of the gyrotropic phase in the transition-metal dichalcogenide semimetal 1T-TiSe2. By shining mid-infrared circularly polarized light on 1T-TiSe2 while cooling it below the critical temperature, we are able to induce the preferential formation of one chiral domain. The chirality of this state is confirmed by measuring an out-of-plane circular photogalvanic current (CPGE), the direction of which depends on the optical induction. Our theory suggests that the generation of CPGE and chiral training arise from the interaction between quantum geometry in the chiral electronic phase and the chiral light. The second example is the helicity-dependent optical control of fully-compensated antiferromagnetic (AFM) order in 2D even-layered MnBi2Te4, a topological Axion insulator. We show that the optical control arises from the optical Axion electrodynamics, which can be visualized as a Berry curvature real space dipole.
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