RUI: Theoretical (Numerical) Investigations of Novel Transport and Topological Properties of Two-Dimensional Interacting Electron Systems

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This project involves theoretical (numerical) approaches to the fundamental nature of new emerging quantum phases and associated novel transport and topological properties in several electron systems. The research will be done at a predominantly undergraduate institution and will afford opportunities for undergraduates and graduate students to participate in the research. The research is comprised of three projects.Firstly, the Principal Investigator (PI) proposes to study the new emerging quantum Hall effect (QHE) in coupled bi-layer electron systems with strong electron-electron interaction. A new quantum phase characterized by the coexistence of integer QHE and exciton condensation has recently been established experimentally, by conducting counter-flow currents in bi-layer systems. Novel fractional QHE states including the non-Abelian paired Hall states are also suggested by experiments. On the theoretical side, it remains an open issue how to characterize quantum Hall states with features besides their charge (total) Hall conductance. A new numerical method based on a matrix of topological invariant Chern numbers has been developed by the PI and her collaborators for this purpose, which will be applied to study the Coulomb drag transport, charge Hall effect and the transport properties in counter-flow current measurement as well as quantum phase transitions in bi-layer systems. We are aiming at understanding the existing experimental observations, characterizing the nature of quantum phase transitions for these new quantum states, and making quantitative predictions regarding transport measurements for future experiments.Secondly, the PI proposes to study the novel QHE of two-dimensional (2D) interacting Dirac fermions in graphene. In recent experiments, a series of QHE plateaus with unconventional quantization rule have been observed for Dirac fermions in single-atom-thick graphite (graphene) system. So far, the interplay of the novel band structure, disorder potential and Coulomb interaction has not been studied yet, which may soon become one of the central topics in the field of QHE. We propose to perform a systematic numerical study using microscopic band model taking into account all these important aspects of the material, which may provide valuable information and further stimulate experimental research.Thirdly, the fundamental problem whether electron-electron interaction can lead to spin-liquid state with topological ordering and fractionalization in 2D electron system will also be investigated numerically. Understanding this issue will have important impact on the theory of strongly correlated electron systems and the future development of the topological quantum computing. We are aiming to identify some concrete examples of topological ordered spin-liquid state in 2D electron systems based on extensive numerical calculations of low energy spectrum, topological degeneracy and spin-spin correlation function.The intellectual merit of this proposal is that the topics addressed are of fundamental importance for the understanding of the new physical phenomena in 2D electron systems. The broader impact on society of the proposed research project is twofold. Firstly, the project will impact on the future development of new magneto-electronic devices and topological quantum computing qubits. Secondly, the present project will provide students and postdoctoral fellows with excellent introduction and training about how to carry out research at the forefront of physics and will also prepare them for dealing with practical problems in future academic and non-academic careers. In the past a few years, PI and her collaborators have developed novel and effective numerical methods, based on topological invariant quantities, to study the quantum transport and topological properties of interacting electron systems. Thus we believe that the proposed research can be carried out effectively and successfully.Non-Technical Abstract: This project involves theoretical (numerical) approaches to the fundamental nature of new emerging quantum phases and associated novel transport and topological properties in several electron systems that are found in solids. The research will be done at a predominantly undergraduate institution and will afford opportunities for undergraduates and graduate students to participate in the research.