Theoretical Problems in Condensed Matter and Statistical Physics

9981283 halperin该奖项支持低温下金属和半导体中受限几何中的电子的理论研究和教育。特别令人感兴趣的是量子霍尔系统和介观系统。量子霍尔系统中特别令人感兴趣的是电子从三维导电区隧穿到量子霍尔系统边缘状态的电流与外加电压数据的理论与实验之间的差异。由于实际系统边缘附近的电子密度分布比通常模型中假设的要复杂，这可能会影响隧穿特性，从而产生差异。PI计划研究更现实的实验系统模型，以更好地了解实际的密度分布。Fermion-Chern-Simons理论将用于确定边界处局域模式的数量，以及当系统大部分处于可压缩量子霍尔态时，确定边缘附近无束缚复合费米子的轨迹和非局域响应函数。其他工作将集中于无序在隧穿量子霍尔系统中的作用，包括在二维电子系统的边缘和内部。重整化组和其他技术将用于检查在可压缩区域中，近局域电子或准粒子态与有限密度的复合费米子态共存的程度，以及这些态的分布如何影响隧道进入层。无序的作用也将被考虑在较高朗道能级中发生的电荷密度波状态，并被用来解释在这些系统中测量到的高度各向异性电阻率。需要解决的一个重要问题是，一个混合区域，其中固定的电荷密度波区域嵌入其他具有未固定电子液体的区域，是否可以解释在各向异性状态下观察到的电阻的大小。其他工作将解决部分满最低朗道能级复合费米子理论形成中的概念问题。在另一个项目中，自旋注入和自旋输运将在介观系统中进行研究。当电子从铁磁性金属注入到普通金属的薄膜或颗粒中时，这一点很重要。自旋松弛的机制将在注入边界和金属的其他地方进行研究。量子干涉发生的情况也将被研究。介观系统的其他工作将是研究近藤体系中量子点抽运现象中的噪声、非线性和耗散效应。将继续研究层间屏障中有针孔的双层系统中库仑阻力现象的理论。该奖项支持凝聚态理论前沿的研究和教育。工作将集中在局限于二维空间的电子上，例如，被困在半导体层中的电子，在强磁场中的电子，以及三维接触中的电子如何隧穿进入和离开电子层。工作还将集中在足够小的材料的电子特性上，这些材料在传导方面存在量子力学效应，例如，与水波发生的干涉效应非常相似。这些是发生在材料中的基本和重要的物理现象；他们的理解可能会导致未来电子设备技术的创新

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.***