Symmetry-Resolved Second Harmonic Generation in Quantum and Functional Materials

Abstract

Second harmonic generation (SHG) has evolved from a probe of noncentrosymmetric crystals into a symmetry-resolved optical method for identifying order parameters in quantum and functional materials. In particular, polarization-resolved rotational anisotropy (RA) measurements of SHG can connect nonlinear susceptibility tensors to the crystallographic and magnetic point groups of the underlying materials. This capability is especially powerful when the ordered state is weak, spatially confined, multipolar, magnetic, or hidden from conventional linear probe techniques. In this review article, we provide a comprehensive overview of RA-SHG studies across a broad range of condensed matter systems. We begin with basic theoretical background for the multipole origins of SHG radiation, the construction of nonlinear susceptibility tensors, and group-theoretical framework connecting tensor components to order parameters. We then review the applications of RA-SHG to polar materials, magnetic orders, and other hidden electronic materials. Finally, we outline challenges and future research directions for using SHG to reveal, image, and control hidden, intertwined, and nonequilibrium phases in quantum and functional materials.