Symmetry-protected nodal points and nodal lines in magnetic materials

Nodal-point and Nodal-line structures in the dispersion of electron energy bands are characterized by their high degeneracy certain corners or lines Brillouin zone (BZ). These nodal can also exist itinerant electrons magnetically ordered materials whose symmetry groups anti-unitary called magnetic space groups. In present work, we provide a complete list which host symmetry-protected nodal-point/line band for spin-1/2 fermionic particles, where degeneracies at points/lines guaranteed irreducible projective representations (IPReps) little co-groups. Our discussion is restricted to point group contains space-time inversion operation $\tilde T=\mathcal IT$, combined spacial $\mathcal I$ time reversal $T$, such that least doubly-degenerate arbitrary points BZ. For these invariants label classes Reps, each class calculate all inequivalent IPReps. From results select out corresponding Rep support high-dimensional ($d\geq$4) We then co-groups have IPReps with factor systems. Examples candidate discussed.