SOS: symmetry-operational similarity

Sang-Wook Cheong

doi:10.1038/s41535-019-0193-9

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.

Highlights

Symmetry appears in all areas of physics
Symmetry and its breaking are quintessential in numerous physical phenomena in condensed matter, such as the appearance of bulk polarization or magnetization through phase transitions, the generation of second harmonic light with strong light illumination, and various nonreciprocal diode effects
Velocity vector (k, linear momentum or wave vector), which is dx/dt where x = displacement and t = time, changes its direction under space inversion as well as time reversal, so it is associated with broken space-inversion and time-reversal symmetries. k can be associated with the motion of quasi-particles such as electrons, spin waves, phonons, and photons in a specimen or the motion of the specimen itself

Summary

Introduction

Symmetry appears in all areas of physics. For example, the local SU (3) × SU(2) × U(1) gauge symmetry and its spontaneous symmetry breaking is the essence of the standard model encompassing quarks, the τ neutrino and the Higgs boson. Since {R, I, M} operations do link the left and right situations, specimen constituents with electric polarization (or field), having broken {R, I, M}, as well as all nonreciprocal cases with broken {R, I, M} + {T} in Fig. 1 can exhibit nonreciprocal electronic transport effects.

Results

Conclusion