Pinch-point singularities in spectroscopy guarantee topological criticality

Electron and magnon bands with topological features have been a major interest in condensed matter physics in the past few decades. In this work we discuss how to identify topologically critical gap-closing points from energy and momentum-resolved spectroscopy without any additional knowledge of the system. More explicitly, observing an n-fold pinch point on two bands with a gapless point sufficiently guarantees that the gapless point is topologically critical, with local Berry curvature n*Pi encoded at the pinch point. These results offer deepr insight and generalization on the theoretical study of two-fold pinch points on magnon bands, which focused on their "dynamical spin ice" nature [1,2].

We will survey the materials in which these features have already been seen (but not brought to attention in some cases): FeSe [3], Nd₂Zr₂O₇ [4], and those in which they should appear in corresponding experiments. Given their wide appearance, the pinch points could be a very useful tool to quickly identify topological bands.

[1] Benton, Phys. Rev. B 94, 104430
[2] Yan et. al., Phys. Rev. B 98, 140402(R)
[3] Wang et al., Nature Materials 4686
[4] Petit et al., Nature Physics 3710