The net charge at interfaces between insulators

Abstract

The issue of the net charge at insulating oxide interfaces is shortly reviewed with the ambition of dispelling myths of such charges being affected by covalency and related charge density effects. For electrostatic analysis purposes, the net charge at such interfaces is defined by the counting of discrete electrons and core ion charges, and by the definition of the reference polarisation of the separate, unperturbed bulk materials. The arguments are illustrated for the case of a thin film of LaAlO$_3$ over SrTiO$_3$ in the absence of free carriers, for which the net charge is exactly 0.5$e$ per interface formula unit, if the polarisation response in both materials is referred to zero bulk values. Further consequences of the argument are extracted for structural and chemical alterations of such interfaces, in which internal rearrangements are distinguished from extrinsic alterations (changes of stoichiometry, redox processes), only the latter affecting the interfacial net charge. The arguments are reviewed alongside the proposal of Stengel and Vanderbilt [Phys. Rev. B {\bf 80}, 241103 (2009)] of using formal polarisation values instead of net interfacial charges, based on the interface theorem of Vanderbilt and King-Smith [Phys. Rev. B {\bf 48}, 4442 (1993)]. Implications for non-centrosymmetric materials are discussed, as well as for interfaces for which the charge mismatch is an integer number of polarisation quanta.