Finding new phases of matter and understanding their physics are primary goals of condensed matter physics. Advances in quantum physics can in turn breed novel technologies, benefiting our society. Topological states are new phases of matter characterized by a nonzero topological invariant. They can support protected surface/edge states, realize elusive particles, and respond to electric and magnetic fields in unconventional ways. On a more fundamental level, topological physics arise from the geometric properties of the quantum wavefunction, i.e., quantum geometry, which include Berry curvature, Berry connection, quantum metric, etc.

First, I will describe how we search for material platforms that support new topology and quantum geometry. In particular, I will focus on our theoretical prediction and experimental observation of the first Weyl fermion semimetal state in TaAs and later the topological chiral crystal state in RhSi. Second, I will describe nonlinear optoelectronic and transport measurements that can probe Berry curvature and interaction in a symmetry-sensitive way. Specifically, I will show how we use mid-infrared photocurrents to probe the chirality of Weyl fermions and other Berry curvature physics in 3D and 2D topological materials. I will also show our photocurrent detection of a novel electronic instability, the gyrotropic order, in the correlated semimetal TiSe2, and how we use circularly polarized light to manipulate such order via quantum geometrical responses. In the final part, I show how current works suggest ample new exciting possibilities to discover fundamental physics in topological condensed matter physics, which also offers pathways to quantum sensing, information and computation technologies.

Watch a video of the talk here.