Hidden topology lurks in seemingly featureless insulators

Trivial insulators with no broken symmetry or topological order still possess hidden topological structure in their phase diagrams, encoded in higher-dimensional generalizations of Berry phases. The researchers computed these textures using non-abelian geometry and found that singularities in them—called diabolical points—mark where the band gap closes and robust edge modes appear. This suggests that even featureless phases are subtly richer than expected, with clear experimental signatures in how boundary states move across phase space.