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

该职业奖支持对量子物质和电子材料拓扑状态的理论研究，其中电子相互作用强烈。在铜和铝等普通金属中，杂质通常对电流传导有害。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。他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，迄今为止所研究的拓扑材料大多局限于三维空间的周期性晶体。PI将超越这一限制，通过理论上研究和设计更一般的非周期性或具有扩展缺陷的结构来扩展拓扑材料的景观。总的目标是从理论上研究这些系统的电子行为，这可能最终导致量子计算和高效电力传输的技术进步。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介绍的开放获取在线学习模块，以撰写未来的本科水平综述文章；（ii）建立一个涉及当地本科学院和HBCUs的外展计划，随后在理哈伊（Lehigh）举办一个有10-15人参加的校园小型研讨会；(3)从少数族裔和代表性不足的社区中挑选本科学生作为导师，目标是吸引他们从事STEM学科的职业。本职业奖支持拓扑凝聚态物理前沿的理论研究，重点关注其一些关键局限性。PI将通过在准晶体及其有理近似上构建低维投影拓扑膜，将拓扑材料的分类扩展到三维以外。当晶体暴露于时间周期驱动时，晶格缺陷，如位错和晶界，也将作为识别动态领域中一类新的平移活性Floquet拓扑相的工具。PI将展示非晶材料，如非晶网络、分形和准晶，用于实现拓扑超导体。与此同时，PI将计算非阿贝尔狄拉克材料中强电子相互作用的特征，如石墨烯基范德华异质结构和分数狄拉克材料。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介绍的开放获取在线学习模块，以撰写未来的本科水平综述文章；（ii）建立一个涉及当地本科学院和HBCUs的外展计划，随后在理哈伊（Lehigh）举办一个有10-15人参加的校园小型研讨会；(3)从少数族裔和代表性不足的社区中挑选本科学生作为导师，目标是吸引他们从事STEM学科的职业。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.