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

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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.