Quantum Effects in Low-Dimensional Systems

University Of California-San Diego, La Jolla CA

Investigators

Abstract

TECHNICAL SUMMARY This award supports theoretical research and education in condensed matter physics. The two central research topics are (i) strongly fluctuating quantum magnetism, typically in low dimensions, and (ii) transport and interfacial physics in graphene and graphite. The major objective in the magnetism work is to characterize the physics of quantum-disordered phases using several approaches. One such approach is through the use of quantum entanglement spectra, which have been shown to yield detailed information regarding the edge excitations of fractional quantum Hall effect states. This line of analysis exploits some deep connections between the fractional quantum Hall effect and spin chains. Partitioning the fractional quantum Hall effect wavefunctions in angular momentum space is equivalent to a reciprocal momentum space partitioning of the corresponding spin chain wavefunctions, and reveals information about the bulk excitation spectra in certain gapless systems. Another direction of this research is in the generalization of valence bond solid states and an investigation of their properties, such as the "hidden" string order in the S=1 Affleck, Kennedy, Lieb, and Tasaki chain, which is emblematic of the Haldane phase. Generalizations to SU(N) spins and to singlets extended over N-site simplices will be investigated, along with corresponding higher-dimensional fractional quantum Hall effect wavefunctions. The work on graphene will focus on junctions and interfaces in graphene and graphite, including junctions between monolayer and bilayer graphene, and also with graphane. The effects of periodic potentials will be studied, both with and without external fields. In graphite, the c-axis transport of the turbostratic material will be modeled, along with the electronic structure of crystalline dislocations. The educational elements of this work include the training of a graduate student and the development of detailed, book-quality, lecture notes for graduate students and advanced undergraduates. NONTECHNICAL SUMMARY This award supports theoretical research and education in condensed matter physics. The research effort will focus on two main topics: (i) magnetism at the microscopic level, and (ii) graphene, which is a one-atom-thick planar sheet of carbon atoms. A common thread is that many of the systems studied are intrinsically one-dimensional or two-dimensional. Low-dimensional quantum magnetism has provided the condensed matter community with some remarkable and compelling paradigms of "quantum-disordered" phases - states of matter where quantum mechanical fluctuations, even at the lowest possible temperatures, lead to a "melting" of classical order. At issue is how to characterize these disordered phases. A recent approach uses entanglement, an intrinsically quantum-mechanical concept, to characterize such states. Deep connections between one-dimensional quantum magnets and two-dimensional electron gases in a strong magnetic field will also be exploited and investigated. Graphene has an unusual electronic structure, in which charge carrying excitations behave as if they are massless, reminiscent of photons, the quanta of light. The research effort here will focus on large-scale inhomogeneities in graphene, including interfaces between single and multilayer graphene, and disruptions in the stacking pattern of graphite. In both cases, the consequences for electronic conduction will be investigated. This is fundamental research that contributes to the intellectual foundations of future device technologies. Graphene, in particular, has unique properties that make it a promising material for various applications including future electronic devices. The educational aspects of this proposal include the training of a PhD student in physics, and the further development of an extensive collection of detailed, book-quality lecture notes for advanced undergraduates and physics graduate students.