Abstract
Spin-space groups (SSGs) have garnered significant attention in recent years due to their higher symmetries and the exotic phenomena they exhibit. In the representation space of fermion wavefunctions, the spin symmetry induces a projective representation, mapping SO(3) to SU(2). Consequently, SSGs naturally emerge as symmetry groups characterized by projective representations.
In this work, we develop a comprehensive projective representation theory to classify the factor systems of symmetry groups. We demonstrate that projective representations give rise to nonsymmorphic Brillouin zones, which differ fundamentally from those arising in conventional representations. These nonsymmorphic Brillouin zones often exhibit unique topological properties. To explore these properties, we extend the symmetry-based indicators theory, which traditionally only applies to standard representations. Our corrections adapt the theory to projective representations, enabling its application in the search for topological materials within SSGs.
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