CAREER: Novel platforms for topology and non-Fermi liquids: From projected topological branes to non-Abelian and fractional materials

非技术总结这个职业奖支持对量子物质和电子材料的拓扑态的理论研究，在这些材料中，电子之间存在强烈的相互作用。在铜和铝等普通金属中，杂质通常不利于电流传导。另一方面，拓扑材料具有特殊的载流通道，对杂质的影响非常强大。它们还提供了一个可能实现量子计算的平台，并为未来在电子领域的应用铺平了道路。然而，迄今研究的拓扑材料大多局限于三维空间中的周期晶体。PI将突破这一局限，通过从理论上研究和设计更一般的非周期结构或具有扩展缺陷的结构来扩展拓扑材料的视野。该奖项的总体目标是从理论上研究这类系统的电子行为，最终可能导致量子计算技术的进步和高效的电力传输。该奖项还支持PI的教育和外展活动。PI将(I)开发关于拓扑凝聚态物理教学导论的开放式在线学习模块，作为未来本科水平的回顾文章，(Ii)建立一个涉及当地本科院校和HBCU的外展计划，随后在LeHigh举办一个有10-15人参加的校园迷你研讨会，以及(3)指导来自少数族裔和代表性不足社区的选定本科生，目标是吸引他们从事STEM学科的职业。PI通过在准晶及其有理近似上构造低维投影拓扑膜，将拓扑材料的分类扩展到三维以外。当晶体暴露在时间周期驱动下时，晶格缺陷，如位错和晶界，也将作为工具来识别动态领域中一类新的平移活跃的Floket拓扑相。PI将展示非晶态材料，如非晶态网络、分形和准晶，以实现拓扑超导体。同时，PI将计算非阿贝尔狄拉克材料中强电子相互作用的特征，例如基于石墨烯的范德华异质结构和分数狄拉克材料。该奖项还支持国际和平协会的教育和外展活动。PI将(I)开发关于拓扑学凝聚态物理教学导论的开放式在线学习模块，导致未来的本科水平的回顾文章，(Ii)建立一个涉及当地本科学院和HBCU的扩展计划，随后在LeHigh举办一个有10-15人参加的校园迷你研讨会，以及(3)指导来自少数族裔和代表不足的社区的选定本科生，目标是吸引他们从事STEM学科的职业。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research into topological states of quantum matter and electronic materials in which electrons interact strongly. In ordinary metals, like copper and aluminum, impurities are usually detrimental to current conduction. Topological materials, on the other hand, have special current carrying channels that are exceptionally robust to the effects of impurities. They also provide a platform that may realize quantum computation and pave the way for future applications in electronics. However, topological materials that have so far been investigated are mostly limited to periodic crystals in three spatial dimensions. The PI will go beyond this limitation and extend the landscape of topological materials by theoretically studying and designing more general structures that are non-periodic or have extended defects in them. The general aim is to theoretically investigate the electronic behavior of such systems which may eventually lead to technological advances in quantum computation and efficient electric power transmission.This award also supports the PI's educational and outreach activities. The PI will (i) develop open access online learning modules on pedagogical introduction to Topological Condensed Matter Physics, leading to a future undergraduate level review article, (ii) build an outreach program involving local undergraduate colleges and HBCUs, followed by an on-campus mini-workshop at Lehigh with 10-15 attendees, and (3) mentor selected undergraduate students from minority and underrepresented communities with the goal of attracting them to careers in STEM disciplines.TECHNICAL SUMMARYThis CAREER award supports theoretical investigations at the forefront of topological condensed matter physics, focused on some of its key limitations. The PI will extend classification of topological materials beyond three dimensions by constructing lower-dimensional projected topological branes on quasicrystals and their rational approximants. Lattice defects, such as dislocations and grain boundaries, will also serve as tools to identify a new class of translationally active Floquet topological phases in the dynamic realm, when crystals are exposed to time periodic drives. The PI will showcase non-crystalline materials, such as amorphous networks, fractals, and quasicrystals, for realizing topological superconductors. In parallel, the PI will compute hallmarks of strong electronic interactions in non-Abelian Dirac materials, such as graphene-based van der Waals heterostructures and fractional Dirac materials. This award also supports the PI's educational and outreach activities. The PI will (i) develop open access online learning modules on pedagogical introduction to Topological Condensed Matter Physics, leading to a future undergraduate level review article, (ii) build an outreach program involving local undergraduate colleges and HBCUs, followed by an on-campus mini-workshop at Lehigh with 10-15 attendees, and (3) mentor selected undergraduate students from minority and underrepresented communities with the goal of attracting them to careers in STEM disciplines.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.