Exploring the twist paradigm in topological and interacting quantum matter

当两个周期结构，如晶格，以一个小的扭转组合在一起时，组合系统形成一个莫尔晶格，其周期可以比原来的晶体长得多。这一众所周知的现象最近在石墨烯中得到了惊人的利用，两层之间的微小扭曲形成了一个双层，导致了各种各样的新量子现象。在这种云纹晶格的背景下运动的电子已经被证明形成了几个新的相，包括相关绝缘体、拓扑带、磁体和超导体。除了作为基本智力挑战的吸引力之外，这些相位很容易通过门控和扭转角控制进行调节，已经被讨论为从自旋电子学到拓扑量子计算等技术应用的有前途的候选者。尽管石墨烯的丰富程度令人惊叹，但人们可能会认为，扭曲石墨烯的物理性质只是冰山一角：事实上，许多其他二维材料在扭曲的情况下组装起来，可以形成有趣的结构。在最近的研究中，从理论上讨论了扭曲过渡金属二硫族化合物、拓扑绝缘体和高tc铜超导体中新物理的可能性，这表明这种新范式的范围和范围可能更广。类似的物理现象在异质层中也有讨论，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，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马约拉纳粒子，以及相关的陈氏绝缘体，它展示了其他独特的和技术上令人满意的品质。

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.