Charge transfer in superlattices consisting of SrIrO$_3$ and SrMnO$_3$ is investigated using density functional theory. Despite the nearly identical work function and non-polar interfaces between SrIrO$_3$ and SrMnO$_3$, rather large charge transfer was experimentally reported at the interface between them. Here, we report a microscopic model that captures the mechanism behind this phenomenon, providing a qualitative understanding of the experimental observation. This leads to unique strain dependence of such charge transfer in iridate-manganite superlattices. The predicted behavior is consistently verified by experiment with soft x-ray and optical spectroscopy. Our work thus demonstrates a new route to control electronic states in non-polar oxide heterostructures.
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