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Materials with tunable charge and lattice degrees of freedom provideexcellent platforms for investigating multiple phases that can be controlledvia external stimuli. We show how the charge-ordered ferroelectric oxideAg$_2$BiO$_3$, which has been realized experimentally, presents a uniqueexemplar of a metal-insulator transition under an external electric field. Ourfirst-principles calculations, combined with a symmetry analysis, reveal thepresence of a nearly ideal hourglass-Dirac-semimetal state in the nonpolarstructure of Ag$_2$BiO$_3$. The low-energy band structure consists of twohourglasslike nodal lines located on two mutually orthogonal glide-mirrorplanes in the absence of spin-orbit coupling (SOC) effects. These lines crossat a common point and form an interlinked chainlike structure, which extendsbeyond the first Brillouin zone. Inclusion of the SOC opens a small gap in thenodal lines and results in two symmetry-enforced hourglasslike Dirac points onthe $\tilde{\mathcal{C}}_{2y}$ screw rotation axis. Our results indicate thatAg$_2$BiO$_3$ will provide an ideal platform for exploring theferroelectric-semiconductor to Dirac-semimetal transition by the application ofan external electric field.

Topological Hourglass Dirac Semimetal in the Nonpolar Phase of Ag$_2$BiO$_3$