Strongly Correlated Low-Dimensional Systems

新的生长和制造技术，加上化学和静电掺杂，使固体中电子的控制和操纵成为可能。例子包括从化学合成的半导体纳米线到掺杂的七叶树球晶体。在许多有趣的情况下，流动电子的运动被样品几何或强晶格通约性效应有意地限制。在这些条件下，相关效应被强烈增强，并有可能转变为“局域”莫特或维格纳晶体态。接近这种局域相的流动电子经常表现出不寻常的行为，这显然与标准费米液体理论相冲突。解开这些微妙的关联效应，并在这些技术上重要的系统中识别潜在的物理现象，是一项艰巨的挑战。在这个理论奖中，相关电子的量子物理将通过关注局域域附近甚至局域域内的行为来探索。具体而言，将研究以下内容：在接近超导体的碳纳米管中输运，研究Luttinger液体相关性与超导邻近效应之间的相互作用；高朗道能级下单层和双层量子霍尔系统中单向电荷密度波（条纹相）的研究。目标是通过利用手性Luttinger液体和复合费米子方法之间的联系来描述这些相中的条纹间准粒子动力学；通过涡旋扩散对超导体进行量子无序化，继续发展描述铜酸盐赝隙的理论框架——更广泛地说，是莫特绝缘体。特别是，二维玻色金属的物理和影响，“二维量子玻色子的正常（非超）流体，将被探索；获得和分析具有大环交换相互作用的二维电子的微观模型，这些电子表现出分数化的量子相。我们感兴趣的是粒子的统计和拓扑秩序的实验意义。新的生长和制造技术，加上化学和静电掺杂，使固体中电子的控制和操纵成为可能。例子包括从化学合成的半导体纳米线到掺杂的七叶树球晶体。在许多有趣的情况下，流动电子的运动被样品几何或强晶格通约性效应有意地限制。在这些条件下，相关效应被强烈增强，并有可能转变为“局域”莫特或维格纳晶体态。接近这种局域相的流动电子经常表现出不寻常的行为，这显然与标准费米液体理论相冲突。解开这些微妙的关联效应，并在这些技术上重要的系统中识别潜在的物理现象，是一项艰巨的挑战。在这个理论奖中，相关电子的量子物理将通过关注局域域附近甚至局域域内的行为来探索。这些结果将具有重大的根本意义，并将影响基于这些现象的设备的发展

New growth and fabrication techniques, together with chemical and electrostatic doping, are enabling an unprecedented control and manipulation of electrons in solids. Examples range from chemically synthesized semiconductor nanowires to doped buckeyball crystals. In many cases of interest the motion of itinerant electrons is intentionally restricted by sample geometry or by strong lattice commensurability effects. Under these conditions, correlation effects are strongly enhanced and transitions into "localized" Mott or Wigner crystal states are possible. Itinerant electrons proximate to such localized phases often exhibit unusual behavior, in apparent conflict with standard Fermi liquid theory. Disentangling the subtle correlation effects and identifying the underlying physics in such technologically important systems presents a formidable challenge.In this theoretical award, the quantum physics of correlated electrons will be explored by focusing on the behavior near, or even in, the localized regime. Specifically, the following will be studied:Transport in carbon nanotubes proximate to superconductors, studying the interplay between Luttinger liquid correlations and superconducting proximity effects;Studying unidirectional charge density waves (stripe phases) in single- and bi-layer quantum Hall systems at higher Landau levels. The goal is to describe the interstripe quasi-particle dynamics in such phases by exploiting the connections between chiral Luttinger liquid and composite Fermion approaches;Continuing to develop a theoretical framework for describing the pseudogap regime of the cuprates - and Mott insulators more generally - by quantum disordering a superconductor via a proliferation of vortices. In particular, the physics and implications of the 2D Bose metal," a normal (non-super) fluid of 2D quantum bosons, will be explored;Obtaining and analyzing microscopic models of 2D electrons with large ring exchange interactions which exhibit fractionalized quantum phases. O finterest are the statistics of the particles and the experimental implications of the topological order.%%%New growth and fabrication techniques, together with chemical and electrostatic doping, are enabling an unprecedented control and manipulation of electrons in solids. Examples range from chemically synthesized semiconductor nanowires to doped buckeyball crystals. In many cases of interest the motion of itinerant electrons is intentionally restricted by sample geometry or by strong lattice commensurability effects. Under these conditions, correlation effects are strongly enhanced and transitions into "localized" Mott or Wigner crystal states are possible. Itinerant electrons proximate to such localized phases often exhibit unusual behavior, in apparent conflict with standard Fermi liquid theory. Disentangling the subtle correlation effects and identifying the underlying physics in such technologically important systems presents a formidable challenge.In this theoretical award, the quantum physics of correlated electrons will be explored by focusing on the behavior near, or even in, the localized regime. The results will be of great fundamental interest and will also influence the development of devices based on these phenomena.***