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，拓扑起着重要的作用，因为物质的这些相的特征是在材料参数的平滑变形下保持不变的某些物理量。因此，此类相的许多物理性质本质上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。这些金属表面状态本质上对杂质等缺陷具有弹性。这种所谓的表面态拓扑保护被认为是一种有前途的新技术途径。 另一方面，强相互作用电子系统中的拓扑材料的研究相对较少。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具有强相关性的系统。在当前的提案中，首席研究员（PI）建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 的目标是在这些新相的理论模型和实际材料之间建立直接联系。找到此类相的优点在于，它们可以在体相和表面中实现强大且独特的电子/磁性特性，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 的团队在这一研究领域开创了新的方向，并开发了几种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 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。利用拓扑材料的不寻常表面状态，PI 还将探索拓扑系统和传统系统之间的工程界面状态。这些练习将为理论和实验带来巨大的智力挑战，并通过未来的技术应用（例如在下一代计算机中执行某些计算任务的全新方法）产生重大的社会影响。

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.