Insulator-to-Metal Transitions Driven by Quantized Formal Polarization Mismatch

We propose a mechanism for insulator-to-metal (IM) transitions driven by the mismatch of quantized formal polarization (QFP), a symmetry-protected bulk invariant. For a material with a low-symmetry insulating phase and a high-symmetry phase that allow distinct QFPs, any continuous path connecting them while preserving the symmetry of the low-symmetry phase must inevitably pass through an IM transition. The reason is that QFP remains invariant along any gapped symmetry-preserving evolution, whereas the high-symmetry phase requires a different QFP, which can only be accommodated by gap closing. First-principles calculations on two representative systems, two-dimensional InPS$_3$ and three-dimensional CdBiO$_3$, confirm this mechanism. Our results establish QFP mismatch as a general symmetry constraint on phase evolution and reveal a new route to symmetry-driven IM transitions in high-symmetry materials.