CAREER: Fractal Bandstructure by Superlattice Patterning

摘要：本NSF职业奖将资助一项围绕石墨烯分形霍夫施塔特能谱的实验研究的研究和推广计划。大约30年前，道格拉斯·霍夫施塔特从理论上证明，当电子同时暴露在磁场和周期性电场中时，会产生递归的自相似行为。这种复杂的图案被称为霍夫施塔特的蝴蝶，是物理学中发现的第一批分形图案之一，但它的实验实现至今仍难以捉摸。在最近的一项突破性发现中，PI开发了新技术，首次在石墨烯基设备中对蝴蝶光谱进行了明确的观察。分形系统代表了一种新的复杂材料，它可能使二维系统的新基础研究成为可能，也为纳米级器件工程提供了新的方向。这个研究项目非常适合初级水平的学生有意义的参与，因为制造和测量可以在有限的高级物理知识下快速学习。除了为纽约城市学院（位于哈莱姆的少数族裔服务机构）的本科生提供研究机会外，该项目还将扩大与当地高中的合作伙伴关系，为大学预科学生提供纳米技术领域的实践培训。通过讲座、研讨会和研究实习机会的结合，该计划的目的是在早期培养对纳米科学的兴趣，努力促进和扩大美国在未来几十年发展创新技术方面的作用。CCNY与周边社区之间关系的一个独特优势是能够进一步针对传统上代表性不足的群体的年轻学生。技术摘要：这项NSF职业奖将资助一项围绕石墨烯/氮化硼异质结构器件的分形霍夫施塔特能谱的实验研究和推广计划。大约40年前，道格拉斯·霍夫施塔特（Douglas Hofstadter）从理论上预测，同时受到磁场和空间周期性电场作用的电子表现出分形行为。在最近的一项突破性发现中，PI证明了将石墨烯与六方氮化硼接触所产生的云纹图案为霍夫施塔特分形谱的实验实现提供了理想尺寸的超晶格潜力。将这些制造技术与低温/高磁场输运测量相结合，PI将利用石墨烯/h-BN平台对预测的量子分形进行首次系统实验研究。这项工作将解决几个突出的和基本的问题，如光谱对超晶格的大小和对称性的依赖；混乱的影响；对称性破缺的本质；以及由于强电子相互作用而产生相关行为的可能性。这个研究项目非常适合初级水平的学生有意义的参与，因为制造和测量可以在有限的高级物理知识下快速学习。除了为纽约城市学院（位于哈莱姆的少数族裔服务机构）的本科生提供研究机会外，该项目还将扩大与当地高中的合作伙伴关系，为大学预科学生提供纳米技术领域的实践培训。通过讲座、研讨会和研究实习机会的结合，这个项目的目的是在早期培养对纳米科学的兴趣，努力促进和扩大美国在未来几十年在发展创新技术方面的作用。CCNY与周边社区之间关系的一个独特优势是能够进一步针对传统上代表性不足的群体的年轻学生。

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.