  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, etc.) 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, etc.) 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.
