Inverse layer capacitance in perovskite oxide superlattices

Ferroelectricity is one of the most important functionalities that can be tuned in perovskite oxide superlattices. At fixed displacement field $D$, the overall polar instability can be accessed by the inverse of the capacitance per basal area as $C^{-1}=\partial V / \partial D$, where $V$ is the potential drop across the supercell.\footnote{M. Stengel, D. Vanderbilt, and N.A. Spaldin, Nature Mater. {\bf 8}, 392 (2009).} Here we propose that $C^{-1}$ can be further rigorously decomposed into contributions from individual AO or BO$_2$ layers, giving an {\it layer inverse capacitance} defined as $c_j^{-1}=\epsilon_0^{-1}(h_j+D\partial h_j/\partial D - \partial p_j/\partial D)$, where $h_j$ and $p_j$ are the layer height and Wannier-based layer polarization\footnote{X. Wu, O. Di\'{e}huez, K.M. Rabe and D. Vanderbilt, Phys. Rev. Lett. {\bf 97}, 107602 (2006).} of layer $j$, respectively. We compute the $c_j^{-1}$ in several typical multicomponent perovskite superlattices such as CaTiO$_3$/BaTiO$_3$ and PbTiO$_3$/SrTiO$_3$, and demonstrate that they satisfy a {\it locality} principle: their behavior depends mainly on the local chemical environment (i.e., the identities of neighboring layers). Thus, we show that the $c_j^{-1}$ can provide an insightful {\it local} analysis of the ferroelectric tendency at interfaces in functional oxide superlattices.