We study a class of topological materials which in their momentum-space band structure exhibit three-fold degeneracies known as triple points. Focusing specifically on $mathcal{P}mathcal{T}$-symmetric crystalline solids with negligible spin-orbit cou
pling, we find that such triple points can be stabilized by little groups containing a three-, four- or six-fold rotation axis, and we develop a classification of all possible triple points as type-A vs. type-B according to the absence vs. presence of attached nodal-line arcs. Furthermore, by employing the recently discovered non-Abelian band topology, we argue that a rotation-symmetry-breaking strain transforms type-A triple points into multi-band nodal links. Although multi-band nodal-line compositions were previously theoretically conceived and related to topological monopole charges, a practical condensed-matter platform for their manipulation and inspection has hitherto been missing. By reviewing the known triple-point materials with weak spin-orbit coupling, and by performing first-principles calculations to predict new ones, we identify suitable candidates for the realization of multi-band nodal links in applied strain. In particular, we report that an ideal compound to study this phenomenon is Li$_2$NaN, in which the conversion of triple points to multi-band nodal links facilitates largely tunable density of states and optical conductivity with doping and strain, respectively.
The search for novel topological phases of matter in quantum magnets has emerged as a frontier of condensed matter physics. Here we use state-of-the-art angle-resolved photoemission spectroscopy (ARPES) to investigate single crystals of Co$_3$Sn$_2$S
$_2$ in its ferromagnetic phase. We report for the first time signatures of a topological Weyl loop. From fundamental symmetry considerations, this magnetic Weyl loop is expected to be gapless if spin-orbit coupling (SOC) is strictly zero but gapped, with possible Weyl points, under finite SOC. We point out that high-resolution ARPES results to date cannot unambiguously resolve the SOC gap anywhere along the Weyl loop, leaving open the possibility that Co$_3$Sn$_2$S$_2$ hosts zero Weyl points or some non-zero number of Weyl points. On the surface of our samples, we further observe a possible Fermi arc, but we are unable to clearly verify its topological nature using the established counting criteria. As a result, we argue that from the point of view of photoemission spectroscopy the presence of Weyl points and Fermi arcs in Co$_3$Sn$_2$S$_2$ remains ambiguous. Our results have implications for ongoing investigations of Co$_3$Sn$_2$S$_2$ and other topological magnets.
We extend the scope of Kitaev spin liquids to non-Archimedean lattices. For the pentaheptite lattice, which results from the proliferation of Stone-Wales defects on the honeycomb lattice, we find an exactly solvable non-Abelian chiral spin liquid wit
h spontaneous time reversal symmetry breaking due to lattice loops of odd length. Our findings call for potential extensions of exact results for Kitaev models which are based on reflection positivity, which is not fulfilled by the pentaheptite lattice. We further elaborate on potential realizations of our chiral spin liquid proposal in strained $alpha$-RuCl$_3$.
