Fig. 3: The simulated topological polar states in PTO thin films.

a f₁₁ vs. E_[001] and b f₁₂ vs. f₁₁ “phase diagrams” of the polar states. f₁₂ and f₄₄ are both set to 0 V in a. f₄₄ and E_[001] are set to 0 V and –1.25 MV/cm in b, respectively. Eight polar patterns near the top (001) planes of the thin film are shown in c. Due to the degeneracy of d1H-SkL (v1H-SkL) and d2H-SkL (v2H-SkL), the regions marked with d1H-SkL (v1H-SkL) in the phase diagrams should also stabilize d2H-SkL (v2H-SkL). The conditions for each state in c are: H-L (f_ij = 0 V and E_[001] = 0 MV/cm), TH-L (f₁₁ = 2 V, f₁₂ = f₄₄ = 0 V and E_[001] = 0 MV/cm), T-L (f₁₁ = 3 V, f₁₂ = f₄₄ = 0 V and E_[001] = 0 MV/cm), TH-SkL (f₁₁ = 3 V, f₁₂ = f₄₄ = 0 V and E_[001] = –1.00 MV/cm), iH-SkL (f_ij = 0 V and E_[001] = –1.25 MV/cm), v1H-SkL (f₁₁ = 1 V, f₁₂ = f₄₄ = 0 V and E_[001] = –1.25 MV/cm), d1H-SkL (f₁₁ = f₁₂ = 4 V, f₄₄ = 0 V and E_[001] = –1.25 MV/cm), and T-SkL (f₁₁ = 3 V, f₁₂ = f₄₄ = 0 V and E_[001] = –1.25 MV/cm).