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

Abstract

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.

Figures (5)

• Figure 1: (a)--(c) Top views of $\ce{InPS3}$ in different phases: (a) L1 phase, (b) H phase, and (c) L2 phase. The two In atoms are labeled for distinction. (d) Variation of polarization along the transition pathway, with the dashed line denoting the metallic state. (e) Variation of direct (red line) and indirect band gap (blue line) along the transition pathway.
• Figure 2: Projected band structure of $\ce{InPS3}$ along the transition pathway. Blue and red indicate contributions from In$_1$ and In$_2$, respectively. (a) Initial state L1: the occupied states near the Fermi level are dominated by In$_1$, while the unoccupied states are mainly derived from In$_2$. (b) Intermediate state between L1 and H: the occupied and unoccupied states approach each other and exhibit mixed contributions from In$_1$ and In$_2$. (c) High-symmetry intermediate state H: the contributions from the two In atoms become identical due to symmetry-enforced degeneracy.
• Figure 3: Top view of the crystal structure and partial charge density distribution of $\ce{InPS3}$. The two In atoms are labeled as In$_1$ and In$_2$. (a) Initial state L1 with polarization $(2/3,1/3)$, where the electronic states are predominantly localized on In$_1$. (b) High-symmetry state H, where the charge density is equally distributed over the two In atoms. (c) Final state L2, where the electronic states are predominantly localized on In$_2$.
• Figure 4: Crystal structure of the primitive cell of $\ce{CdBiO3}$ and the evolution of its electronic properties along the transition pathway. (a)–(c) Top views of the three representative phases: (a) L1, (b) H, and (c) L2. The two Bi atoms are labeled for distinction. (d) Evolution of polarization along the transition pathway, with the dashed line indicating the metallic state. (e) Evolution of the direct and indirect band gaps along the transition pathway.
• Figure 5: Projected band structure of $\ce{CdBiO3}$ along the transition pathway. Blue and red indicate contributions from Bi$_1$ and Bi$_2$, respectively. (a) Initial state L1: the highest valence band is mainly derived from Bi$_1$, while the lowest conduction band is dominated by Bi$_2$. (b) Intermediate state between L1 and H: the occupied and unoccupied states approach each other, with mixed contributions from Bi$_1$ and Bi$_2$. (c) High-symmetry intermediate state H: the contributions from the two Bi atoms become identical due to symmetry-enforced degeneracy.