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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. Here, by using first-principles calculations, we demonstrate that the experimentally synthesized nonmagnetic HgPbO$_3$ represents a unique example of such hybrid emph{Weyl ferroelectric semimetal}. Its centrosymmetric $Rbar{3}c$ phase will undergo a ferroelectric phase transition to the ferroelectric $R3c$ structure. Both phases are metallic and the ferroelectric phase owns a spontaneous polarization of 33 $mu$C/cm$^2$. Most importantly, it also harbors six pairs of chiral Weyl nodes around the Fermi level to be an oxide WSM. The structural symmetry broken phase transition induces a topological phase transition. 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 external pulse electric field, which is promising for potential applications of integrated topotronic and ferroelectric devices.
The quest for nonmagnetic Weyl semimetals with high tunability of phase has remained a demanding challenge. As the symmetry breaking control parameter, the ferroelectric order can be steered to turn on/off the Weyl semimetals phase, adjust the band s
Weyl semimetals are a class of materials that can be regarded as three-dimensional analogs of graphene breaking time reversal or inversion symmetry. Electrons in a Weyl semimetal behave as Weyl fermions, which have many exotic properties, such as chi
As one of Weyl semimetals discovered recently, NbP exhibits two groups of Weyl points with one group lying inside the $k_z=0$ plane and the other group staying away from this plane. All Weyl points have been assumed to be type-I, for which the Fermi
The Weyl semimetal exhibits various interesting physical phenomena because of the Weyl points, i.e., linear band-crossings. We show by Floquet theory that a linearly polarized light applied to a band insulator can induce controllable Weyl points. In
Band-crossings occurring on a mirror plane are compelled to form a nodal loop in the momentum space without spin-orbit coupling (SOC). In the presence of other equivalent mirror planes, multiple such nodal loops can combine to form interesting nodal-