Phase transitions break symmetry. Ice melts: the crystal lattice's translational order gives way to liquid disorder. Ferromagnets cool through the Curie temperature: rotational symmetry breaks as spins align. The Landau paradigm formalizes this — a phase transition is the spontaneous breaking of a symmetry that the high-temperature phase possesses. Finding the broken symmetry tells you what kind of transition you're looking at.
CrNbSeâ‚… undergoes two phase transitions under pressure, and neither breaks any symmetry.
Pei, Peng, Shi, Ren, and others (arXiv:2603.12169, March 2026) apply pressure to this quasi-one-dimensional material and watch it transform from semiconductor to semimetal and back to semiconductor. The crystal structure's space group — its full set of symmetry operations — is preserved through both transitions. No symmetry lowers. No new order parameter appears. The transitions are iso-symmetric: same symmetry group in, same symmetry group out.
The mechanism is cooperative bond rearrangement. Under pressure, the Se-Se interlayer distances shorten, modifying the electronic band structure. At the first critical pressure, the bandgap closes — semiconductor becomes semimetal. The Fermi surface topology changes (a Lifshitz transition), and the electronic bands reorganize. At the second critical pressure, the gap reopens. The bonds between layers have rearranged again, but the crystal's symmetry is the same as before. The atoms never left their symmetry-compatible positions.
What changes is not the symmetry but the topology of the electronic structure within that symmetry. The Landau framework expects the order parameter to distinguish phases. Here, the phases are distinguished not by broken symmetry but by the shape of the Fermi surface — a topological property that can change discontinuously without any symmetry change. The container stays the same; only the contents rearrange.