Abstract
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 coupling, 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 multiband nodal links. Although multiband 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 multiband 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 multiband nodal links facilitates largely tunable density of states and optical conductivity with doping and strain, respectively.
Highlights
The recent rapid developments in the topological band theory of crystals [1,2,3,4,5,6,7,8,9,10,11,12] and engineered metamaterials [13,14,15,16,17] fueled a fruitful research into topological band degeneracies in semimetals and metals
Focusing on PT -symmetric crystalline solids with negligible spin-orbit coupling, we find that such triple points can be stabilized by little groups containing a three, four, or sixfold 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
By employing the novel insights of non-Abelian quaternion charges, we illuminate a relation between the nodal lines (NLs) and triple points (TPs) topology; in particular, we show that type-A TPs in spinless PT -symmetric models generally evolve into multiband nodal links (Fig. 2) under rotation-symmetry-breaking perturbations [60]
Summary
The recent rapid developments in the topological band theory of crystals [1,2,3,4,5,6,7,8,9,10,11,12] and engineered metamaterials [13,14,15,16,17] fueled a fruitful research into topological band degeneracies in semimetals and metals. We investigate the interplay of TPs and non-Abelian band topology, and we suggest a platform to experimentally observe multiband nodal links in TP materials under strain To obtain these results, we develop a symmetry-based classification of TPs in spinless PT -symmetric systems into type A or B (Fig. 1) similar to the SOC case. By employing the novel insights of non-Abelian quaternion charges, we illuminate a relation between the NL and TP topology; in particular, we show that type-A TPs in spinless PT -symmetric models generally evolve into multiband nodal links (Fig. 2) under rotation-symmetry-breaking perturbations [60]. From the perspective of the non-Abelian invariant the path γ0 cannot be shrunk to a point on the other side of the TP due to the presence of the NL (red in Fig. 2) in the adjacent energy gap This suggests a nontrivial value q(γ0) = +1 characterizing the NL composition around the type-A TP.
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