Patrick A. Lee - US grants

9813764
Lee
This award supports research and education in the area of strong correlations and disorder. Three problems will be considered: (1) The metal-to-insulator transition in two dimensions. A focus of research in this area is to take into account the role of strong interactions and disorder, and to ascertain the role of local moment formation in the metallic state near the transition. (2) The effect of non-magnetic impurities in spin 1/2 antiferromagnets for which quantum fluctuations are important. Of particular inspiration is the theoretical and experimental observation of a surprising purely quantum mechanical effect: long-range order induced by introducing impurities in ladder compounds. The PI inquires whether related phenomena occur in the two-dimensional spin 1/2 Heisenberg model, and plans to study the effect of disorder and of an external magnetic field. (3) The PI proposes to continue work on the effect of disorder in d-wave superconductors.
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This award supports research on phenomena and ordered states (e.g. superconductivity) involving electrons that interact strongly with each other in materials that show significant random deviations from perfect crystalline order. The understanding of these phenomena are of fundamental importance and bears on a wide class of materials of potential importance to future device technologies that includes electrons trapped at interfaces between semiconductors, and high temperature superconductors and their relatives. This research activity provides for continued education of advanced students and post-graduates in state-of-the-art methods and concepts in the theory of solid state materials.
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The field of mesoscopic physics has had significant progress during the past few years. The theoretical progress has been driven by the statistical approach to sample fluctuations in the ensemble of small disordered systems. As the sizes of the systems are made smaller and smaller, eventually they approach the electron mean free path. Then the motion of an electron becomes ballistic. On the other hand, due to the complex geometry, this motion can still be chaotic. Such a system is similar in many respects to other systems (atomic or nuclear) which display quantum chaos. For analytical calculations disordered systems turn out to be simpler than chaotic ballistic ones because of the additional ensemble averaging. The idea of this research is to use disordered systems as a laboratory for the investigation of quantum chaos. In a diffusive regime we plan to derive relations and develop analytical methods which can be extended to general cases. Theoretical studies will also be carried out on problems of persistent currents in isolated rings and the magnetic susceptibility of isolated metallic grains - problems closely connected to quantum chaos. We will take into account interactions between electrons since existing one-electron theories are in substantial disagreement with experiment. %%% The field of mesoscopic physics is a very current one which deals with basic problems in fundamental physics and yet has important ramifications for microelectronics. The present research will theoretically deal with a number of problems in mesoscopic physics. In particular, the research will study the onset of quantum chaos in these systems. Clearly, besides its fundamental importance, the conditions under which a microelectronic system becomes chaotic, or unstable, is of interest to the computer and communications industry.

This award supports theoretical research and education on the quantum theory of localized magnetic moments in diverse electronic environments in solids. Specific areas of research include the physics of geometric frustration of quantum magnetism in insulating materials and the interplay between possibly frustrated inter-moment exchange and coupling between local moments and conduction electrons in metallic materials. Emphasis will be on understanding low temperature phenomena where quantum mechanical effects dominate. The PI aims to clarify the nature of the ground states and low energy excitations suggested by experiments or numerical calculations on several low-dimensional insulating frustrated quantum magnets. Field theoretical methods will be developed with an aim to obtaining physical insight. The PI will explore whether frustrated quantum magnets display excitations with fractional quantum numbers. The PI seeks to bridge the gap between theory and experiments in this active area of condensed matter physics. The PI will also study Kondo lattice models for metallic systems with localized magnetic moments, for example LiVO. Various phenomena discovered in these systems originate in the competition between possibly frustrated magnetic exchange between the local moments and the interaction between the local moments and the conduction electrons.
This award also supports education at the graduate level in advanced theoretical condensed matter physics. The PI plans to involve undergraduate students in the research.
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This award supports fundamental theoretical condensed matter physics research on phenomena that arise from geometrical frustration of quantum magnetic materials and the interaction between magnetic moments localized on particular atomic sites with itinerant conduction electrons. Geometrical frustration occurs when the interactions between magnetic moments cannot be simply satisfied because of the geometrical arrangement of the moments on the crystal lattice. This is fundamental research in an active and challenging area that involves strongly correlated electron materials including heavy fermion materials and quantum magnets like Cs2CuCl4. Research in this area has revealed subtle and beautiful phenomena in condensed matter physics and provides the intellectual foundation for future materials and device technologies. This award also supports education at the graduate level in advanced theoretical condensed matter physics. The PI plans to involve undergraduate students in the research.
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The NSF Convergence Accelerator supports use-inspired, team-based, multidisciplinary efforts that address challenges of national importance and will produce deliverables of value to society in the near future. This project seeks to develop approaches that address issues of decoherence and crosstalk by scalable topological superconductors (TSC). Investigation for achieving realistic large-scale quantum computers is required to advance the field of quantum information science. This project will integrate Majorana zero modes (MZMs) into conventional superconducting qubit architectures to advance their application to quantum computing. By having outreach programs towards K-12 students and research experiences for undergraduates, this project will broaden participation in quantum with a focus on underrepresented minorities.

The project will build and establish a cross-sector team that will develop advances in controlling the topological nature of materials to advance quantum computing to deliver fault-tolerant qubits and their quantum interconnects. This project seeks (1) to understand and demonstrate the non-local topological nature of the MZMs by detecting the electron teleportation through a pair of MZMs; (2) to establish the basic elements for measuring the parity state in a teleportation-based T-qubit; (3) to explore flux quantization caused by a supercurrent loop that is mediated by the MZMs and set up the basic flux (or pseudo-spin) measurements of a T-qubit; (4) to identify and plan the Phase II research program, and (5) to build a strong team of academic, governmental lab, and industrial partners. Building on recent developments of a new TSC material platform, this project aims to demonstrate the quantum nature and the non-local topological protection of MZMs in the platform as well as build topological qubits that can be integrated into existing quantum computing circuitry. This may lead to greater functionality in superconducting circuits which can significantly advance topological quantum computing. The project deliverable includes a platform supporting topological qubit that is more robust and more scalable. By establishing a nationwide student exchange program and outreach activities to K-12 students, this project seeks to engage students in quantum research and training to broaden participation.

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.