Reaching for an upper bound in the nonlinear optical conductivity of solids

Synopsis

A major theme in the past couple of decades of research in condensed matter physics-archive has been to understand properties of quantum materials using the language of geometric (or “Berry”) phases and connections. Nonlinear optical properties, such as second harmonic generation, are examples of phenomena that depend crucially on the band structure geometry. In this talk, I will report on the recent discovery of the highest-known second harmonic susceptibility in the topological metal compound TaAs. I will further present a new theorem which relates a sum rule for the second order nonlinear conductivity with the third cumulant (or “skewness”) of the electronic wavefunction. This theorem suggests the existence of ultimate upper bounds allowed on the nonlinear optical conductivity of crystalline materials.