CAREER: Unconventional superconductivity and disordered criticality in two dimensions

University Of California-Davis, Davis CA

Investigators

Abstract

NON-TECHNICAL SUMMARY This CAREER award supports theoretical research and education aimed at understanding quantum phases of electrons in two-dimensional materials, with a focus on superconductivity and disorder. Although certain phases of matter are well-described in colloquial terms, for example liquid or solid, the fundamentally quantum nature of the universe supports a multitude of states beyond those we see in everyday life. The quantum nature of these phases often results in incredible properties; for instance, a superconducting system conducts without resistance, allowing electricity to be transported over arbitrary distances without energy loss. Recent experimental progress offers an exciting opportunity to improve our understanding of quantum systems whose electrons interact with each other strongly (i.e., the electrons strongly ``feels'' the presence of their peers), a class of systems that have historically been very difficult to describe theoretically. Experimentalists have achieved unprecedented control over the fabrication of two-dimensional materials such as graphene (an intrinsically two-dimensional material composed of carbon) and assemblies made from them, allowing the construction of systems that realize a variety of quantum phases. These developments support a relatively rapid interplay between theory and experiment, which this project will exploit to improve our general understanding of quantum matter. Specifically, this project aims to: (1) Develop a unified understanding of the superconducting phases seen in a variety of distinct graphene structures, systems constructed by stacking graphene in different ways. The PI will use a variety of theoretical techniques to investigate models for superconductivity based on features common to all superconducting graphene systems. (2) Characterize quantum phase transitions in 2D with disorder, such as impurities and other imperfections in the arrangement of atoms. Disorder is an unavoidable feature of all material systems. Quantum phase transitions are driven by quantum fluctuations in contrast to more familiar transitions like ice to water that are driven by thermal fluctuations. The PI will specifically focus on the transitions separating two quantum phases of matter, where disorder can have especially subtle consequences. Integrated within this research project is a multi-level plan aimed at promoting physics to underrepresented groups both before and during undergraduate education. Specifically, the PI will (i) foster early interest in condensed matter among high school students by developing and teaching a course about 2D quantum materials for a summer Science Apprenticeship program at River City High; (ii) encourage and support aspiring young scientists at both a high school and undergraduate level through a partnership with various mentoring programs; and (iii) initiate an undergraduate peer-mentoring program aimed at students belonging to underrepresented groups. TECHNICAL SUMMARY This CAREER award supports theoretical research and education into experimentally accessible properties of two-dimensional (2D) quantum phases of matter, focusing on superconducting graphene and the interplay of disorder and criticality. Theories of highly entangled quantum states of matter---their characterization and classification---have seen great strides in the past several decades. By contrast, an understanding of the prerequisites needed to physically realize these states and the criteria to identify them is lagging. An opportunity to narrow the gap between physical materials and theoretical understanding has recently arisen in the form of groundbreaking experimental developments in the synthesis and manipulation of true 2D materials, which have resulted in the discovery of a multitude of systems displaying a wide variety of correlated phases. The best-studied of these 2D systems are the van der Waals materials: not only can many different van der Waals systems be stacked in a nearly arbitrary fashion, but the twist angle between layers can also be specified. For sufficiently small twist angles, the result is a moiré superlattice orders of magnitude larger than the microscopic crystal of the constituent atoms. These advances provide a new set of tuning parameters---gating, stacking, and twist angle---to exploit in the pursuit of characterizing and understanding the ensuing quantum phenomena. The result is a relatively rapid interplay between theory and experiment, which this project will leverage in order to better understand the role of interactions, disorder, and their interplay in 2D systems. The specific aims of the project are: (1) The development of a unified understanding of superconducting graphene systems. Superconductivity has been observed in numerous graphene systems, both with and without moiré superlattices. The PI will investigate both the identity of the normal state parent to the superconductor as well as the superconducting pairing glue itself through a mix of analytical and numerical techniques. (2) An improved characterization and understanding of quantum critical points in 2D with disorder, drawing inspiration from recent experiments. The PI will both compute experimentally relevant observables as well as investigate the more formal question of disorder at a weak first order transition. Integrated within this research project is a multi-level plan aimed at promoting physics to underrepresented groups both before and during undergraduate education. Specifically, the PI will (i) foster early interest in condensed matter among high school students by developing and teaching a course about 2D quantum materials for a summer Science Apprenticeship program at River City High; (ii) encourage and support aspiring young scientists at both a high school and undergraduate level through a partnership with various mentoring programs; and (iii) initiate an undergraduate peer-mentoring program aimed at students belonging to underrepresented groups. 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.