Exploring the twist paradigm in topological and interacting quantum matter

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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.