Fig. 3: Polar order and response of the PbTiO3/SrTiO3 superlattices.
From: Giant voltage amplification from electrostatically induced incipient ferroelectric states
a–h, Simulation results for the 3/3 (a–d) and 9/9 (e–h) superlattices, as a function of epitaxial strain. Panels a and e show two superlattice averages of the polarization: \(\left|{P}_{z}\right|\) corresponds to averaging the absolute value of the z-component of the local polarizations, so as to get a non-zero result in the multi-OOP state; Px is the direct supercell average of the x-component of the local polarizations, where x is the modulation direction (perpendicular to the domain walls) in the multi-OOP and mixed states. Panels b and f show two components, χxx and χzz, of the (global) dielectric susceptibility tensor. Panels c and g show the inverse permittivity \({\epsilon }_{{{{\rm{f}}}}}^{-1}\) in units of \({\epsilon }_{0}^{-1}\) (left axis) and screening factor φf (right axis) of the ferroelectric layer. Panels d and h show the voltage ratio \({{{{\mathcal{A}}}}}_{{{{\rm{d}}}}}\) of the dielectric. The grey zone in panels a–d marks the region where both multi-OOP and mono-IP states are (meta)stable. Dark-coloured down-pointing triangles correspond to multi-OOP states, while we use light-coloured stars for mixed states and empty up-pointing triangles for mono-IP states.
