Non-Technical Abstract:<br/>Most of what we know about materials comes from their response to perturbations at their favorite (natural) frequencies. For instance, the pitch of sound from a plucked violin string depends on its length, the tension in it, and its thickness. In a similar way, the behavior of atoms in materials depends on the natural frequency, which, for many solid materials, fall in the Terahertz spectral range, a very difficult range to access technically until recently. This project takes advantage of recent dramatic technical advances in Terahertz frequencies to probe new materials called topological materials. These materials have been predicted to possess properties that make them useful for developing electronic devices for quantum information technology. This project also includes a broad initiative in education and outreach. The work is of particular educational value in training students with unique skills to prepare them as the work force in high tech industries. The research team will play active roles in the Johns Hopkins Physics Fair- an outreach activity which brings hundreds of people each year through Hopkins' labs during a Saturday event and exposes them to various physics demonstrations and activities. The team will also give demonstration shows at the Physics Fair and work with under-resourced local schools.<br/><br/>Technical Abstract:<br/>This is a project to investigate a number of topological and other material systems that have important Berry phase effects using nonlinear optical response. Topological states of matter have been of central interest in condensed matter physics in recent years, yet we are lacking unique measures of many of these systems' electrodynamic properties. Theory has indicated that the nonlinear response of these compounds can give unique insight into the essential Berry phase structure of their underlying wavefunctions. Measurements will emphasize the extended THz range (here 0.1 – 40 THz [0.4 – 165 meV]) where generally responses target the low energy emergent degrees of freedom, but experiments will use a full complement of photon energies up through the near infrared. Experiments will be performed on both topological materials and trivial materials with important Berry phase effects. Materials include topological insulators, Weyl semimetals, Dirac semimetals, and 2D transition metal dichalcogenides. We will explore the nonlinear response of these system to both linear and circularized polarized radiation in a number of specific configurations that are designed to elucidate their Berry phase structure (Berry curvature and Berry connection) in these compounds. Many theoretical predictions exist, but experimentally, this is an almost completely unexplored area, which aside from its intrinsic importance has the potential to give major new insight into what might have been considered a mature area — the nonlinear response of solids.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.