Berry-phase theory of polar discontinuities at oxide-oxide interfaces

In the framework of the modern theory of polarization, we rigorously establish the microscopic nature of the electric displacement field $\mathbf{D}$. In particular, we show that the longitudinal component of $\mathbf{D}$ is preserved at a coherent and insulating interface. To motivate and elucidate our derivation, we use the example of LAO/STO interfaces and superlattices, where the validity of the above conservation law is not immediately obvious. Our results generalize the “locality principle” of constrained-$\mathbf{D}$ density-functional theory to the first-principles modeling of charge-mismatched systems.

Figure 1

(Color online) Schematic representation of formal polarization in the [(a) and (b)] bulk and at [(c) and (d)] interfaces. Blue (thick gray) and red (thin gray) vertical lines represent ${\text{BO}}_2$ and AO layers in a (a) II-IV perovskite; green (light gray) and brown (dark gray) are the same but in a (b) III-III perovskite. Black circles represent electronic Wannier centers, which carry a charge of $-1$ (not all are explicitly shown). Different choices of basis (grouping) lead to values of $P$ differing by $\Delta P=e/S$. (c) Choice of basis such that no charges are left in the interface region. (d) Choice of bias leaving net-neutral interface region (shaded gray area).

Figure 2

(Color online) Top panel: cation-oxygen rumplings ${\delta }_{\text{AO}}$ and ${\delta }_{\text{BO}2}$, in a given layer of the ${\left(\text{LAO}\right)}_4/{\left(\text{STO}\right)}_4$ superlattice. The red (dark gray) boxes indicate the grouping of the layers adopted for defining $P_j$ and ${\tilde{P}}_j$. Bottom panel: cell polarizations ${\tilde{P}}_j$ (open symbols), $P_j$ (filled symbols), and macroscopic value $P_{\text{Berry}}$ (dashed horizontal line).