The study of complex oxides and oxide heterostructures has dominated the field of experimental and theoretical condensed matter research for the better part of the last few decades. Powerful experimental techniques such as molecular beam epitaxy and pulsed laser deposition have made fabrication of oxide heterostructures with atomically sharp interfaces possible, whereas more and more sophisticated handling of exchange and correlations within first principles methods including density functional theory (DFT) supplemented with Hubbard U corrections and hybrid functionals, and beyond DFT techniques such as dynamical mean field theory (DMFT) have made understanding of such correlated oxides and oxide interfaces easier. The emergence of the high-mobility two-dimensional electron gas with fascinating properties such as giant photoconductance, large negative magnetoresistance, superconductivity, ferromagnetism, and the mysterious coexistence of the latter two have indeed caught the attention of condensed matter community at large. Similarly, strain tuning of oxides have generated considerable interest particularly after the recent discovery of piezoelectric methods of strain generation. Theoretical understanding and prediction of the possible exotic phases emerging in such complex oxides both under strain and in heterostructures will eventually lead to better design of device applications in this new emerging field of oxide electronics, along with possible discovery of exotic physics in condensed matter systems, which may be of wider significance! In this review, we briefly look at theoretical studies of novel phenomena in oxides under strain and oxide heterostructure, and try to understand the role of exchange and particularly correlation in giving rise to such exotic electronic states. This review though primarily focuses on the theoretical aspects on understanding the different mechanism of the phenomena of emergence of exotic phases, does provide a unique overview of the experimental literature as well, accompanied by the theoretical understanding such that relevant device applications can be envisaged.

中文翻译：

---

了解应变和氧化物异质结构下复杂氧化物中交换和相关性的作用

在过去几十年的大部分时间里，复合氧化物和氧化物异质结构的研究一直主导着实验和理论凝聚态研究领域。强大的实验技术，如分子束外延和脉冲激光沉积，使得制造具有原子尖锐界面的氧化物异质结构成为可能，而在包括密度泛函理论 (DFT) 和 Hubbard U 校正的第一原理方法中，交换和相关性的处理越来越复杂和混合泛函，以及超越动态平均场理论 (DMFT) 等 DFT 技术，使得对这种相关氧化物和氧化物界面的理解更加容易。具有巨大光电导等迷人特性的高迁移率二维电子气的出现，大的负磁阻、超导、铁磁性以及后两者的神秘共存确实引起了凝聚态界的普遍关注。类似地，氧化物的应变调谐已经引起了相当大的兴趣，特别是在最近发现了应变产生的压电方法之后。对在应变和异质结构下在这种复杂氧化物中出现的可能奇异相的理论理解和预测最终将导致在这个新兴的氧化物电子领域中更好地设计器件应用，以及可能在凝聚态系统中发现奇异物理，这可能具有更广泛的意义！在这篇综述中，我们简要介绍了应变和氧化物异质结构下氧化物中新现象的理论研究，并尝试理解交换的作用，尤其是相关性在产生这种奇异的电子态中的作用。这篇综述虽然主要集中在理解异相出现现象的不同机制的理论方面，但也提供了对实验文献的独特概述，并伴随着理论理解，从而可以设想相关的器件应用。