Cheong SW, Huang FT, Kim M. Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products.
REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022;
85:124501. [PMID:
36198263 DOI:
10.1088/1361-6633/ac97aa]
[Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 10/05/2022] [Indexed: 06/16/2023]
Abstract
The symmetry of the whole experimental setups, including specific sample environments and measurables, can be compared with that of specimens for observable physical phenomena. We, first, focus on one-dimensional (1D) experimental setups, independent from any spatial rotation around one direction, and show that eight kinds of 1D objects (four; vector-like, the other four; director-like), defined in terms of symmetry, and their dot and cross products are an effective way for the symmetry consideration. The dot products form a Z2× Z2× Z2group with Abelian additive operation, and the cross products form a Z2× Z2group with Abelian additive operation or Q8, a non-Abelian group of order eight, depending on their signs. Those 1D objects are associated with characteristic physical phenomena. When a 3D specimen has symmetry operational similarity (SOS) with (identical or lower, but not higher, symmetries than) an 1D object with a particular phenomenon, the 3D specimen can exhibit the phenomenon. This SOS approach can be a transformative and unconventional avenue for symmetry-guided materials designs and discoveries.
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