CAREER: Fractal Bandstructure by Superlattice Patterning

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Non-Technical Abstract:This NSF Career Award will fund a research and outreach program centered around the experimental study of the fractal Hofstadter energy spectrum in graphene. Nearly 30 years ago, Douglas Hofstadter showed theoretically that when electrons are exposed to both a magnetic field and a periodic electric field, a recursive self similar behaviour results. Known as Hofstadter's Butterfly, this complex pattern represents one of the first fractal patterns discovered in Physics, and yet its experimental realization has since remained elusive. In a recent breakthrough discovery, the PI developed new techniques that enabled the first unambiguous observation of the butterfly spectrum in graphene-based devices. The fractal system represents a new kind of complex material that may enable new fundamental studies of patterned two-dimensional systems, as well as new directions in device engineering at the nanoscale. This research program is ideally suited to meaningful involvement by junior level students, since the fabrication and measurement can be quickly learned with limited knowledge of advanced physics. In addition to providing research opportunities for undergraduates at The City College of New York (CCNY), a minority serving institution located in Harlem, this program will expand partnerships with local area high-schools to provide hands-on training to pre-university aged students in the area of nanotechnology. Through a combination of lectures, workshops and research placements opportunities, this program is aimed at generating interest in nanoscience at an early age in an effort to promote and expand America's role in developing innovative technology in the coming decades. A unique advantage of the relationship between CCNY and its surrounding community is the ability to further target this program towards young students from traditionally underrepresented groups.Technical Abstract:This NSF Career Award will fund a research and outreach program centered around the experimental study of the fractal Hofstadter energy spectrum in graphene/boron nitride heterostructures devices. Nearly 40 years ago Douglas Hofstadter theoretically predicted that electrons subjected simultaneously to a magnetic field and spatially periodic electric field exhibit fractal behaviour. In a recent breakthrough discovery the PI demonstrated that the moire pattern resulting from placing graphene in contact with hexagonal boron nitride provides the ideal-sized superlattice potential for experimental realization of Hofstadter's fractal spectrum. Combining these fabrication techniques together with low temperature/high magnetic field transport measurements, the PI will utilize the graphene/h-BN platform to perform the first systematic experimental investigation of the predicted quantum fractal. This effort will address several outstanding and fundamental questions, such as the dependence of the spectrum on both the magnitude and symmetry of the superlattice; the influence of disorder; the nature of symmetry breaking; and the possibility of correlated behaviour due to strong electron interactions. This research program is ideally suited to meaningful involvement by junior level students, since the fabrication and measurement can be quickly learned with limited knowledge of advanced physics. In addition to providing research opportunities for undergraduates at The City College of New York (CCNY), a minority serving institution located in Harlem, this program will expand partnerships with local area high-schools to provide hands-on training to pre-university aged students in the area of nanotechnology. Through a combination of lectures, workshops and research placement opportunities, this program is aimed at generating interest in nanoscience at an early age in an effort to promote and expand America's role in developing innovative technology in the coming decades. A unique advantage of the relationship between CCNY and its surrounding community is the ability to further target this program towards young students from traditionally underrepresented groups.