Topology and Correlation in Quantum Materials

最近，在理解弱相互作用电子系统中物质的所谓拓扑相方面取得了巨大的进展。在这里，拓扑起着重要的作用，因为物质的这些相是由某些物理量表征的，这些物理量在材料参数的平滑变形下是不变的。因此，这类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被授予2016年诺贝尔物理学奖。研究最多的拓扑相的例子是拓扑绝缘体，其中材料的主体是电惰性的，但表面是金属的。这些金属表面态对杂质等缺陷具有内在的弹性。这种所谓的表面态的拓扑保护被认为是一条很有前途的新技术之路。另一方面，强相互作用电子系统中的拓扑材料相对较少被研究。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关联的系统。在目前的提案中，首席研究员(PI)建议探索强关联量子材料中可能的拓扑相，其中电子相互作用起着根本的重要作用。特别是，PI的目的是在这些新相的理论模型和实际材料之间建立直接联系。找到这样的相的好处是，它们将允许在体相和表面具有强健和特殊的电/磁性质，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态，例如通过磁性，并为新技术提供更灵活的应用。*最近，Pi的团队在这一研究领域开辟了新的方向，并为相关量子材料发展了几个理论模型，其中电子的自旋和轨道自由度之间的强烈纠缠起着关键作用。在这些成果的基础上，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所特有的新的拓扑现象开辟一条新的途径。利用拓扑材料的不同寻常的表面状态，PI还将探索拓扑系统和传统系统之间的工程界面状态。这些练习将给理论和实验带来巨大的智力挑战，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上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.