Theoretical Problems in Condensed Matter and Statistical Physics

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9981283HalperinThis award supports theoretical research and education on electrons in confined geometries, in metals and semiconductors, at low temperatures. Of particular interest are quantum Hall and mesoscopic systems. Of particular interest in quantum Hall systems are discrepancies between theory and experiment for current vs. applied voltage data for electrons tunneling into the edge state of a quantum Hall system from a three-dimensional conducting region. The discrepancies may arise because the electron density profile near the edges of the actual systems is more complicated than assumed in the usual models and this can effect tunneling characteristics. The PI plans to investigate more realistic models of experimental systems, to understand better what the actual density profile is. Fermion-Chern-Simons theory will be used to determine the number of localized modes at the boundary, and also to determine the trajectories and nonlocal response functions of unbound composite fermions near the edge, when the bulk of the system is in a compressible quantum Hall state. Other work will focus on the role of disorder in tunneling into quantum Hall systems, both at the edge and in the interior of the two-dimensional electron system. Renormalization group and other techniques will be used to examine the extent to which nearly localized electron or quasiparticle states can coexist with a finite density of composite fermion states, in a compressible region, and how a distribution of such states may affect tunneling into the layer. The role of disorder will also be considered for the charge-density wave state that has been postulated to occur in higher Landau levels, and which has been invoked to explain the highly anisotropic resistivities measured in these systems. An important question to be addressed is whether a mixture of regions, with pinned charge density wave regions embedded in other regions with an unpinned electron liquid, may explain the magnitude of the electrical resistance observed in the anisotropic state. Other work will address conceptual issues in the formation of composite fermion theory of the partially full lowest Landau level. In another project, spin injection and spin transport will be examined in mesoscopic systems. This is important when electrons are injected from a ferromagnetic metal into a thin film or particle of normal metal. Mechanisms for spin relaxation will be examined at the injecting boundaries and elsewhere in the metal. The circumstances under which quantum interference will occur will also be examined. Other work on mesoscopic systems will be the study of noise, nonlinearities and dissipation effects in pumping phenomena in quantum dots in the Kondo regime. Work will continue on the theory of Coulomb drag phenomena in bilayer systems with pinholes in the barrier between the layers. %%%This award supports research and education at the frontiers of condensed matter theory. Work will focus on electrons confined to two dimensions, e.g. electrons trapped in a layer of a semiconductor, in a strong magnetic field and how electrons in three-dimensional contacts can tunnel into and out of the electron layer.Work will also focus on the electronic properties of materials that are small enough that there are quantum mechanical effects on conduction, e.g. interference effects much like those that take place for water waves. These are fundamental and important physical phenomena that occur in materials; their understanding may lead to innovations for future electronic device technologies.***