Weyl Ferroelectric Semimetal

The recent discoveries of ferroelectric metal and Weyl semimetal (WSM) have stimulated a natural question: whether these two exotic states of matter can coexist in a single material or not. These two discoveries ensure us that physically it is possible since both of them share the same necessary condition, the broken inversion symmetry. By using first-principles calculations, we demonstrate that the experimentally synthesized nonmagnetic HgPbO$_3$ is such a hybrid "Weyl ferroelectric semimetal”. Its centrosymmetric $R$\bar{3}c$ phase will undergo a ferroelectric phase transition to the ferroelectric $R3c$ structure. Both phases are metallic. Most importantly, it also harbors six pairs of chiral Weyl nodes around the Fermi level to be an oxide WSM. The coexistence of ferroelectricity and Weyl nodes in HgPbO$_3$ is an ideal platform for exploring multiphase interaction and mutual control. The Weyl nodes can be tuned by temperature or external pulse electric field, which is promising for potential applications.