Pressure-induced metal-insulator transition in oxygen-deficient LiNbO$_3$-type ferroelectrics

Hydrostatic pressure and oxygen vacancies usually have deleterious effects on ferroelectric materials because both tend to reduce their polarization. In this work we use first-principles calculations to study an important class of ferroelectric materials - LiNbO$_3$-type ferroelectrics (LiNbO$_3$ as the prototype), and find that in oxygen-deficient LiNbO$_{3-\delta}$, hydrostatic pressure induces an unexpected metal-insulator transition between 8 and 9 GPa. Our calculations also find that strong polar displacements persist in both metallic and insulating oxygen-deficient LiNbO$_{3-\delta}$ and the size of polar displacements is comparable to pristine LiNbO$_3$ under the same pressure. These properties are distinct from widely used perovskite ferroelectric oxide BaTiO$_3$, whose polarization is quickly suppressed by hydrostatic pressure and/or oxygen vacancies. The anomalous pressure-driven metal-insulator transition in oxygen-deficient LiNbO$_{3-\delta}$ arises from the change of an oxygen vacancy defect state. Hydrostatic pressure increases the polar displacements of oxygen-deficient LiNbO$_{3-\delta}$, which reduces the band width of the defect state and eventually turns it into an in-gap state. In the insulating phase, the in-gap state is further pushed away from the conduction band edge under hydrostatic pressure, which increases the fundamental gap. Our work shows that for LiNbO$_3$-type strong ferroelectrics, oxygen vacancies and hydrostatic pressure combined can lead to new phenomena and potential functions, in contrast to the harmful effects occurring to perovskite ferroelectric oxides such as BaTiO$_3$.