Transformation from a Multi-type Dirac Semimetal into a Crossed-nodal-ring Semimetal

LiOsO₃ is a ferroelectric metal. Upon lowering temperature, LiOsO₃ undergoes a structural phase transition from the non-ferroelectric R-3c phase to the ferroelectric R3c phase with spontaneously broken inversion symmetry. Here we show that this transition also presents the first case of a topological phase transition between a multi-type Dirac semimetal and a crossed-nodal-ring semimetal. In the high-temperature non-ferroelectric phase, the nonsymmorphic glide mirrors help to stabilize multiple Dirac points close to the Fermi level, including three linear Dirac points at L, and one cubic and two linear Dirac points at T. Across the phase transition into the ferroelectric phase, the broken inversion symmetry transforms each linear Dirac point at L into a nodal ring, and interestingly, transforms the cubic Dirac point at T into three mutually-crossed nodal rings.