Exploring the twist paradigm in topological and interacting quantum matter

当两个周期性结构，例如晶格，以小的扭曲组装时，组合系统形成莫尔晶格，其周期可以比原始晶体长得多。这种众所周知的现象最近在石墨烯中被利用到了惊人的效果，其中形成双层的两层之间的小扭曲导致了各种各样的新颖量子现象。在这种莫尔晶格背景上移动的电子已被证明会形成几个新相，包括相关绝缘体、拓扑带、磁体和超导体。除了他们的上诉作为基本的智力挑战，这些阶段，很容易通过门控和扭转角控制可调，已被讨论作为有前途的候选人的应用范围从自旋电子学的拓扑量子计算技术。尽管其惊人的丰富性，但可能会认为扭曲石墨烯的物理学只是冰山一角：实际上，许多其他二维材料可以预期在扭曲组装时形成有趣的结构。在最近的研究中，已经从理论上讨论了扭曲过渡金属二硫属化物、拓扑绝缘体和高Tc铜酸盐超导体中新物理的可能性，这表明这种新范式的潜在范围和范围要广得多。在异质双层中也讨论了类似的物理现象，即由两种具有不同晶格常数的不同材料组装而成的双层。拟议的研究将寻求扩大材料和现象的空间，在那里扭曲范式可以导致新的或技术上有用的物质状态。这项工作将包括寻找一种难以捉摸的拓扑超导体，一种特殊类型的超导体，能够承载被认为是未来拓扑量子计算应用的基石的Majorana粒子，以及相关的Chern绝缘体，它表现出其他独特的和技术上理想的品质。

When two periodic structures, such as crystal lattices, are assembled with a small twist, the combined system forms a moire lattice whose period can be much longer than the original crystal. This well known phenomenon has been recently exploited to an astonishing effect in graphene where small twist between two layers forming a bilayer leads to a great variety of novel quantum phenomena. Electrons moving on the background of such a moire lattice have been shown to form several new phases, including correlated insulators, topological bands, magnets and superconductors. In addition to their appeal as fundamental intellectual challenge these phases, easily tunable through gating and twist angle control, have been discussed as promising candidates for applications in technologies ranging from spintronics to topological quantum computation. Despite its amazing richness it may be argued that physics of the twisted graphene is but a tip of an iceberg: indeed many other two-dimensional materials can be expected to form interesting structures when assembled with a twist. Possibilities for new physics in twisted transition metal dichalcogenides, topological insulators and high-Tc cuprate superconductors have been discussed theoretically in very recent studies, suggesting a potentially much wider scope and reach of this new paradigm. Similar physics has been discussed in heterobilayers, that is, bilayers assembled from two distinct materials with different lattice constant. The proposed research will seek to expand the space of materials and phenomena where the twist paradigm can lead to new or technologically useful states of matter. This effort will include search for an elusive topological superconductor, a special type of a superconductor capable of hosting Majorana particles that are thought to be building blocks for future applications in topological quantum computing, as well as the correlated Chern insulator which exhibits other unique and technologically desirable qualities.