RUI: Novel Transport Properties in Strongly Interacting Electron Systems

该奖项支持半导体中二维强相互作用电子的基础理论和计算研究和教育。pi将研究金属-绝缘体跃迁（MITs）。人们普遍认为，二维半导体中的零场MIT和高tc超导体中的超导体-绝缘体转变都是由强电子相关性引起的，尽管对这两种转变的微观机制尚未达成共识。本研究的一个中心目标是探索二维相互作用电子的零场MIT是否具有以陈恩数为特征的深刻的拓扑描述。采用精确对角化和密度矩阵重整化群（DMRG）方法研究量子霍尔条纹相。目标是利用波函数的陈氏数描述和多体系统的广义索利斯数方法获得输运性质。这些计算的目的是确定在低温下是否存在一种新的类似液晶的金属相，即近晶相。这些计算旨在阐明无序和量子涨落所起的作用，并深入了解这些强相关电子系统的本质。为了更好地理解耦合两层半导体系统中的库仑拖输运以及纵向和横向自旋输运，pi还将采用基于波函数拓扑表征的新方法，研究强相互作用二维电子双层系统的新输运性质。基于输运性质，确定了双层体系的相图和量子相变的性质。该奖项为加州州立大学北岭分校和山姆休斯顿大学的学生提供教育体验，使他们能够参与研究。该奖项支持半导体中二维强相互作用电子的基础理论和计算研究和教育。pi将使用一种创新的理论方法与计算相结合，在三个领域开展研究，pi将探索：1.随着无序量的增加，电子相关性是否会导致金属态和绝缘态之间的相变；2)层状半导体系统是否可以组合成这样一种方式，即可以操纵层间电子之间的相互作用来控制三维半导体结构中的自旋和电荷的输运；(3)在强垂直磁场中，无序对二维电子量子霍尔态的影响。这些领域中的每一个都涉及到我们对材料中电子状态的理解的基本挑战，并涉及到由于强电子-电子相互作用导致的电子之间的相关性而产生的新现象。这项工作也有助于新一代半导体器件的知识基础。该奖项为加州州立大学北岭分校和山姆休斯顿大学的学生提供教育体验，使他们能够参与研究。＊＊＊

This award supports fundamental theoretical and computational research and education on strongly interacting electrons confined to two-dimensions in semiconductors. The PIs will study metal-insulator transitions (MITs). It is generally believed that strong electronic correlations are responsible for both the zero-field MIT in 2D semiconductors and the superconductor-insulator transition in high-Tc superconductors, although there has been no consensus on the microscopic mechanism for either transition. A central goal of this research is to explore whether the zero-field MIT for interacting electrons in 2D has an insightful topological description characterized by the Chern number. Quantum Hall stripe phases will be studied using exact diagonalization and the density matrix renormalization group (DMRG method). An objective is to obtain transport properties using the Chern number description of the wavefunctions and the generalized Thouless number method for many body systems. These calculations are aimed to determine if there is a new liquid-crystal-like metallic phase, a smectic phase, at low temperature. These calculations are intended to elucidate the role played by disorder and quantum fluctuations and to give insight into the nature of these strongly correlated electron systems. The PIs will also use a new method based on the topological characterization of the wavefunction, to study novel transport properties of double layer systems of strongly interacting two dimensional electrons in order to better understand Coulomb drag transport, and longitudinal and transverse spin transport in coupled two layer semiconductor systems. Based on transport properties, the phase diagram and the nature of quantum phase transitions in double layer systems will be determined.This award supports educational experiences for students at California State University Northridge and Sam Houston University enabling them to participate in research. %%%This award supports fundamental theoretical and computational research and education on strongly interacting electrons confined to two-dimensions in semiconductors. The PIs will use an innovative theoretical approach combined with computation to carry out research in three areas, where the PIs will explore: 1.) whether electronic correlations can give rise to a phase transition between metallic and insulating states as the amount of disorder is increased; 2.) whether layered semiconductor systems can be combined in such a way that the interactions between electrons between layers can be manipulated to control the transport of spin and charge in three dimensional semiconductor structures; 3.) the effect of disorder on quantum Hall states of electrons confined to two-dimensions in a strong perpendicular magnetic field. Each of these areas involves fundamental challenges to our understanding of electronic states in materials and involves novel phenomena that arise as a consequence of the correlations among electrons that result from strong electron-electron interactions. This work also contributes to the intellectual foundations for new generations of semiconductor devices. This award supports educational experiences for students at California State University Northridge and Sam Houston University enabling them to participate in research. ***