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 D. In particular, we show that the longitudinal component of 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-D density-functional theory to the first-principles modeling of charge-mismatched systems.