Triple nodal points characterized by their nodal-line structure in all magnetic space groups

We analyze triply degenerate nodal points [or triple (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when spin-orbit coupling is negligible, and consider TPs formed along high-symmetry lines the momentum space by a crossing three transforming according to 1D 2D irreducible corepresentation (ICR) little co-group. The result complete classification such all magnetic groups, including non-symmorphic ones, several characteristics nodal-line structure at near TP. show that presently studied exhausted 13 point groups (MPGs) can arise as co-group line which support both ICRs. For 10 identified MPGs, TP are uniquely determined without further information; contrast, 3 MPGs containing sixfold rotational symmetry, two types possible, depending choice each illustrated with first-principles calculations concrete material candidate.