Abstract
Symmetry often governs condensed matter physics. The act of breaking symmetry spontaneously leads to phase transitions, and various observables or observable physical phenomena can be directly associated with broken symmetries. Examples include ferroelectric polarization, ferromagnetic magnetization, optical activities (including Faraday and magneto-optic Kerr rotations), second harmonic generation, photogalvanic effects, nonreciprocity, various Hall-effect-type transport properties, and multiferroicity. Herein, we propose that observable physical phenomena can occur when specimen constituents (i.e., lattice distortions or spin arrangements, in external fields or other environments) and measuring probes/quantities (i.e., propagating light, electrons, or other particles in various polarization states, including vortex beams of light and electrons, bulk polarization, or magnetization) share symmetry-operational similarity (SOS) in relation to broken symmetries. In addition, quasi-equilibrium electronic transport processes such as diode-type transport effects, linear or circular photogalvanic effects, Hall-effect-type transport properties ((planar) Hall, Ettingshausen, Nernst, thermal Hall, spin Hall, and spin Nernst effects) can be understood in terms of symmetry-operational systematics. The power of the SOS approach lies in providing simple and physically transparent views of otherwise unintuitive phenomena in complex materials. In turn, this approach can be leveraged to identify new materials that exhibit potentially desired properties as well as new phenomena in known materials.