We study zigzag interfaces between insulating compounds that are isostructural to graphene, specifically II-VI, III-V and IV-IV two-dimensional (2D) honeycomb insulators. We show that these one-dimensional interfaces are polar, with a net density of
excess charge that can be simply determined by using the ideal (integer) formal valence charges, regardless of the predominant covalent character of the bonding in these materials. We justify this finding on fundamental physical grounds, by analyzing the topology of the formal polarization lattice in the parent bulk materials. First principles calculations elucidate an electronic compensation mechanism not dissimilar to oxide interfaces, which is triggered by a Zener-like charge transfer between interfaces of opposite polarity. In particular, we predict the emergence of one dimensional electron and hole gases (1DEG), which in some cases are ferromagnetic half-metallic.
The two-dimensional electron gas (2DEG) at the interface between LaAlO$_3$ (LAO) and SrTiO$_3$ (STO) has become one of the most fascinating and highly-debated oxide systems of recent times. Here we propose that a one-dimensional electron gas (1DEG) c
an be engineered at the step edges of the LAO/STO interface. These predictions are supported by first principles calculations and electrostatic modeling which elucidate the origin of the 1DEG as an electronic reconstruction to compensate a net surface charge in the step edge. The results suggest a novel route to increasing the functional density in these electronic interfaces.
Against expectations, robust switchable ferroelectricity has been recently observed in ultrathin (1 nm) ferroelectric films exposed to air [V. Garcia $et$ $al.$, Nature {bf 460}, 81 (2009)]. Based on first-principles calculations, we show that the sy
stem does not polarize unless charged defects or adsorbates form at the surface. We propose electrochemical processes as the most likely origin of this charge. The ferroelectric polarization of the film adapts to the bound charge generated on its surface by redox processes when poling the film. This, in turn, alters the band alignment at the bottom electrode interface, explaining the observed tunneling electroresistance. Our conclusions are supported by energetics calculated for varied electrochemical scenarios.
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 a
t 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.
The polar interface between LaAlO$_{3}$ and SrTiO$_{3}$ has shown promise as a field effect transistor, with reduced (nanoscale) feature sizes and potentially added functionality over conventional semiconductor systems. However, the mobility of the i
nterfacial two-dimensional electron gas (2DEG) is lower than desirable. Therefore to progress, the highly debated origin of the 2DEG must be understood. Here we present a case for surface redox reactions as the origin of the 2DEG, in particular surface O vacancies, using a model supported by first principles calculations that describes the redox formation. In agreement with recent spectroscopic and transport measurements, we predict a stabilization of such redox processes (and hence Ti 3$d$ occupation) with film thickness beyond a critical value, which can be smaller than the critical thickness for 2D electronic conduction, since the surface defects generate trapping potentials that will affect the interface electron mobility. Several other recent experimental results, such as lack of core level broadening and shifts, find natural explanation. Pristine systems will likely require changed growth conditions or modified materials with a higher vacancy free energy.
The physics of oxide superlattices is considered for pristine (001) multilayers of the band insulators LaAlO3 and SrTiO3 with alternating p and n interfaces. First principles results and a model of capacitor plates offer a simple paradigm to understa
nd their dielectric properties and the insulator to metal transition (IMT) at interfaces with increasing layer thickness. The charge at insulating interfaces is found to be as predicted from the formal ionic charges, not populations. Different relative layer thicknesses produce a spontaneous polarization of the system, and allow manipulation of the interfacial electron gas. Large piezoresistance effects can be obtained from the sensitivity of the IMT to lateral strain. Carrier densities are found to be ideal for exciton condensation.
