Topology and Correlation in Quantum Materials

最近，在理解弱相互作用电子系统中所谓的物质拓扑相方面取得了巨大进展。在这里，拓扑学起着重要的作用，因为物质的这些相在材料参数的光滑变形下具有一定的物理量不变的特征。因此，这种相的许多物理性质天生对材料的各种微观细节不敏感。拓扑相的最初想法最近获得了2016年的诺贝尔物理学奖。拓扑相研究最多的例子是拓扑绝缘体，其中大部分材料是电惰性的，但表面是金属的。这些金属表面状态对杂质等缺陷具有内在的弹性。这种所谓的表面状态拓扑保护被认为是一种有前途的新技术。******另一方面，强相互作用电子系统中的拓扑材料相对较少探索。很明显，我们目前对弱相互作用电子系统的理解不能直接应用于强相关系统。在目前的提案中，首席研究员（PI）提议探索强相关量子材料中可能的拓扑相，其中电子相互作用起着至关重要的作用。特别是，PI旨在将这些新相的理论模型与实际材料直接联系起来。发现这种相的优点是，它们将允许在体和表面具有强大和特殊的电子/磁性，这在弱相互作用的类似物中是不可能的。此外，强电子相互作用将提供额外的旋钮来控制拓扑保护的表面状态，例如通过磁性，并为新技术提供更灵活的应用。******最近，PI的研究小组在这方面开辟了新的研究方向，并开发了几个相关量子材料的理论模型，其中电子自旋和轨道自由度之间的强纠缠起着关键作用。在这些成就的基础上，PI正计划研究相关拓扑相的一般组织原则。这将为理解相关电子材料特有的新拓扑现象开辟一条新途径。利用拓扑材料的不同寻常的表面状态，PI还将探索拓扑和传统系统之间的工程界面状态。这些练习将为理论和实验提供巨大的智力挑战，并通过未来的技术应用产生重大的社会影响，例如在下一代计算机中执行某些计算任务的根本新方法。

Recently, there has been tremendous progress in understanding so--called topological phases of matter in weakly interacting electron systems. Here topology plays an important role in the sense that these phases of matter are characterized by certain physical quantities invariant under smooth deformations of material parameters. As a result, many physical properties of such phases are inherently insensitive to various microscopic details of materials. The initial idea of topological phases has recently been awarded the Physics Nobel prize in 2016. The most studied example of topological phases is topological insulators, where the bulk of the material is electrically inert, but the surface is metallic. These metallic surface states are intrinsically resilient to imperfections such as impurities. This so--called topological protection of surface states is considered a promising route to new technologies. ******On the other hand, topological materials in strongly interacting electron systems are relatively less explored. It has become clear that our current understanding of weakly interacting electron systems cannot directly be applied to systems with strong correlation. In the current proposal, the principal investigator (PI) proposes to explore possible topological phases in strongly correlated quantum materials, where the electron interactions play a fundamentally important role. In particular, the PI aims to make direct connection between theoretical models for these novel phases and real materials. The virtue of finding such phases is that they would allow robust and peculiar electronic/magnetic properties in the bulk and surface, which are not possible in weakly interacting analogs. Further, strong electron interaction would provide additional knobs to control topologically protected surface states, for example via magnetism, and offer more flexible applications to new technologies.******Recently, the PI's group has pioneered new directions in this line of research and developed several theoretical models for correlated quantum materials, where strong entanglement between spin and orbital degrees of freedom of electrons plays a pivotal role. Building on these achievements, the PI is planning to investigate general organizing principles for correlated topological phases. This would open a new avenue in understanding of new topological phenomena, unique to correlated electron materials. Utilizing unusual surface states of topological materials, the PI would also explore engineered interface states between topological and conventional systems. These exercises would offer great intellectual challenges to both theories and experiments, and significant societal impact via future technological applications such as fundamentally new ways to perform certain computational tasks in next generation computers.