Physics Department - Chirality, Planar Chirality and Magnetic Chirality

Abstract
Chirality refers to a property of an object or state in which it cannot be superimposed onto its mirror image, even after applying spatial rotations, translations, or time reversal (T). This indicates that the object breaks all three mirror symmetries in any spatial orientation or position. Since spatial inversion (parity, P) can be expressed as a combination of mirror reflection and a two-fold spatial rotation, true chirality implies the absence of both P and PT (combined parity and time reversal) symmetries. Planar chirality, in contrast, refers to objects that break two—but not all three—mirror symmetries. It is sometimes referred to as ferro-rotation, ferro-axiality, or electro-toroicity. Magnetic chirality describes spin configurations in non-chiral magnetic lattices that lack any mirror symmetry. In this discussion, we explore the emergent physical properties and phenomena associated with chirality, planar chirality, and magnetic chirality. Particular focus will be given to the symmetry requirements underlying both dissipative and non-dissipative behaviors related to these forms of chirality.

References
[1] Permutable SOS (symmetry operational similarity), Sang-Wook Cheong, Seongjoon Lim, Kai Du and Fei-Ting Huang, npj Quantum Mater. 7, 40 (2022).
[2] Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products, Sang-Wook Cheong, Fei-Ting Huang and Minhyong Kim, Rep. Prog. Phys. 85 124501 (2022).
[3] Magnetic chirality, Sang-Wook Cheong, and Xianghan. Xu, npj Quantum Mater. 7, 40 (2022).