Topology from band (co-)representation theory in spinful systems: spin groups and magnetic line groups*

Topological Quantum Chemistry (TQC) has been successful in diagnosing band topology using only the symmetries of the system [1, 2]. We begin extending TQC to magnetic systems in two new ways. First, we derive the elementary band (co-)representations of magnetic line groups. The (magnetic) line groups are often overlooked despite corresponding to symmetries of quasi-1D systems, which are of fundamental importance due to their use as illustrative models as well as being building blocks of higher-dimensional systems [3]. Second, we begin extending TQC to the spin groups – generalizations of magnetic groups – which apply for systems of any degree of spin-orbit coupling. Since the magnetic groups apply only for the case of strong spin-orbit coupling, this work opens the door to examining weak spin-orbit coupled magnetic materials and excitations in them [4-7].

[1] B. Bradlyn et al Topological quantum chemistry Nature 547 298305 (2017)

[2] L. Elcoro et al Magnetic Topological Quantum Chemistry Nat. Commun. 12 5965 (2021)

[3] M. Damnjanovic et al Line Groups in Physics: Theory and applications to nanotubes and polymers. Springer Berline, Heidelberg (2010)

[4] D. Litvin Spin Point Groups Acta. Cryst. (1975)

[5] P. Liu et al Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling. PRX 12 021016 (2022)

[6] A. Corticelli et al Spin-space groups and magnon band topology. PRB 105, 064430 (2022)

[7] N. Lazic et al Spin line groups. Acta. Cryst. A69, 611-619 (2013)