准一维无序体系电子局域化及输运特性

在单电子紧束缚近似下,利用多对角全随机厄米矩阵算法,结合负本征值理论和无限阶微扰理论及传输矩阵方法,研究准一维多链无序体系中电子波函数局域化特性及其电子输运特性。研究结果表明:由于格点能量无序,准一维多链无序体系电子波函数呈现出局域化特性;格点能量无序度减小会导致在中间能区发生退局域化现象,表现为在中间能区电子波函数的局域长度大于体系格点数,即出现扩展态,且出现扩展态的能量区间随着无序度的减小而增大的趋势;同时,随着链数的增加,体系有向退局域化方向发展的趋势;在中间能区电子输运透射系数较大,而在低能区及高能区透射系数较小,同时,格点能量无序与维度效应对体系的电子输运存在竞争效应,当体系格点数及链数一定时,体系的透射系数随着格点能量无序度的增大而减小,而当体系格点数及格点能量无序度一定时,准一维多链无序体系的透射系数随着体系链数的增大而增大。     

一维无序系统电子结构

本文应用负本征值理论方法,计算了含有上万个粒子的一维无序系统的电子态密度,针对无序程度和系统大小等物理量,讨论了无序系统的电子结构。结果表明,随着无序程度的变大,电子的局域化程度加强,而随着无序系统的变大,局域化的电子数增多。     

一维无序体系的振动局域态

 应用点阵动力学的方法以及五对角对阵矩阵本征矢算法,考虑原子间次近邻相互作用,计算了一维无序体系的振动本征态的分布.结果表明与电子本征态分布一样,无序体系的声子态分布也具有局域性,且局域程度与本征频率的大小、体系无序程度以及系统大小有密切的关系.     

无序对准一维矢势束缚中无质量Dirac电子的影响

通过有限差分的方法,数值计算了一个相对论性质的Dirac电子在磁场和无序同时存在时的能谱结构,并讨论了不同磁场强度和无序强度时电子密度分布的变化情况.结果发现:随着无序强度的增大,无序势削弱了磁场对电子的捕获,使局域化现象减弱,使得无质量Dirac电子出现了有别于Anderson局域化的现象.     

二维无序系统的电子性质

用改进了的 Recursion 方法研究二维无序系统的电子性质。计算了二维无序系统的电子态密度、迁移率边界、局域化临界点以及直流电导率。结果表明,与对角无序系统相比,对角及非对角无序系统以及存在次近邻跳跃的系统局域性质均发生变化,非对角无序的影响取决于其大小,而次近邻跳跃的存在总是使电子态趋于延展。     

无序光子局域化材料研究

概述了无序介质光子局域化的研究内容,总结了光子局域化研究中曾使用的材料,推荐了两类可用于中红外光子局域化研究的新材料。     

一维纳米材料中电子局域态分布

从一维纳米随机链模型出发,在考虑近邻、次近邻相互作用的情况下,运用多对角全随机厄米矩阵求解方法计算了一维纳米材料的电子局域态中心位置.针对晶界无序度和晶粒大小,讨论了材料中的电子局域态分布.研究结果表明:局域态中心位置随能量的改变而改变,并且在不同的能量范围内局域态分布不同,在某些能量范围内,能量变化很小而局域位置变化很大,电子跳跃很容易发生,而在另一些能量范围内,能量变化很大但局域位置变化很小,电子跳跃难以发生,因而直接影响材料的导电、导热等性能;晶界无序度和晶粒大小对局域态分布影响很大,当晶界无序度变小时,体系趋向有序,局域态位置随能量的变化呈一定程度的周期性;而当晶粒粒径变小时,晶界的作用增强,无序作用也相应增强,局域态增多,分布密度增大.     

一维光波导阵列的安德逊局域化

采用数值模拟的方法,研究了一维光波导阵列的安德逊模型,结果表明,安德逊模型的引入,会导致光波导阵列光波传导的性质的改变。对角无序导致的局域化现象,导致光波经历一段时间传播后会局域到特定位点。而随着无序度的提高,系统中局域态的数目会增加,而单一局域态的定域化长度会减小。     

准一维系统中Lyapunov指数的性质?

建立了Anderson模型的传输矩阵,并采用传输矩阵法求解了准一维系统中的Lyapuov指数(LE),LE与电子局域化长度成反比,LE很好地描述了电子的局域化性质.通过计算SPS理论中的τ值,研究了在一维系统中成立的标度方程是否适用于准一维系统.本文还给出了多条链中不同通道的LE之间关联的计算方法,计算了2个通道和3个通道之间关联随着系统无序度的变化情况.     

无序和斐波那契序列的二进制波导阵列的安德森局域研究

为了研究相关性对电磁波的安德森局域现象的影响,该文根据无序序列构造了无序一维二进制波导阵列结构、根据斐波那契序列构造了准周期一维二进制波导阵列结构。利用分析转移矩阵方法分别计算了上述2种结构中横电模式的透过率、局域长度和电场的空间分布,并利用一维矩形微波波导进行了相关的实验。根据无序序列构造的无序二进制波导阵列结构的透射共振峰与周期性结构一一对应,位于带边的模式首先转为局域态;根据斐波那契序列构造的准周期二进制波导阵列结构的传输特性与组成阵列的具体单元结构无关,电磁场能量通过分布在空间中不同位置的局域态之间的耦合传输形成离散的传输态。     

Anderson localization of a non-interacting Bose-Einstein condensate

Anderson localization of waves in disordered media was originally predicted fifty years ago, in the context of transport of electrons in crystals. The phenomenon is much more general and has been observed in a variety of systems, including light waves. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization. Here we use a non-interacting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice-a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases.     

无序材料直流电导中的无序作用机理

在单电子紧束缚无序模型基础上，建立一维无序材料电子跳跃输运直流电导率计算模型，并推导其直流电导率计算公式；通过计算材料的直流电导率，分析不同无序形式下无序度对材料直流电导率的影响，探讨无序在材料电子输运中的本质作用。计算结果表明，在对角无序情况下，无序材料的直流电导率随着无序度的增加而减小；当无序度较小时，电导率随材料无序度的变化有振荡行为；非对角无序材料的电导率小于对角无序材料的电导率，同时，在无序度较小的区域，材料的电导率呈现先增大后减小的特性；完全无序材料的电导率大于非对角无序材料的电导率而小于对角无序材料的电导率，且在完全无序情况下材料的电导率随无序度的变化关系与非对角无序情况下电导率随无序度的变化关系很相似；在无序度较大时，无论是对角无序、非对角无序还是完全无序情况下，无序度对电导率的影响均不明显。     

无序对一维费米气体的影响

计算了开边界,均匀系统和有谐振势存在的条件下,一维费米气体的态密度和密度分布,并对干净系统,在位能无序系统和跳跃能无序系统的结果进行比较。从态密度与密度分布的数值计算结果表明：无序使系统趋向于局域化。     

Direct observation of Anderson localization of matter waves in a controlled disorder

In 1958, Anderson predicted the localization of electronic wavefunctions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves, microwaves, sound waves and electron gases. However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose-Einstein condensate released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle. We operate in a regime of pure Anderson localization, that is, with weak disorder-such that localization results from many quantum reflections of low amplitude-and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction-a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one-dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref. 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.     

The microscopic nature of localization in the quantum Hall effect

The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties owing to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential. Transport experiments that probe the extended states in the transition regions between quantum Hall phases have been used to test both the theory and its implications for quantum Hall phase transitions. Although several experiments on highly disordered samples have affirmed the validity of the single-particle picture, other experiments and some recent theories have found deviations from the predicted universal behaviour. Here we use a scanning single-electron transistor to probe the individual localized states, which we find to be strikingly different from the predictions of single-particle theory. The states are mainly determined by Coulomb interactions, and appear only when quantization of kinetic energy limits the screening ability of electrons. We conclude that the quantum Hall effect has a greater diversity of regimes and phase transitions than predicted by the single-particle framework. Our experiments suggest a unified picture of localization in which the single-particle model is valid only in the limit of strong disorder.     

无序度和温度对一维无序体系费米能的影响

从一维情况出发,采用单电子紧束缚无序模型,建立无序体系一定温度下费米能公式,同时考虑到无序体系中无序这一本质要素,通过数值计算探讨不同无序模式下无序度与体系费米能关系,并进一步探讨温度等对体系费米能的影响。结果表明:无序体系的费米能随无序度的增大而减小,并且非对角无序对体系费米能的影响很大,考虑非对角无序时,体系的费米能大大降低;温度对体系费米能的影响表现为,随温度的升高,体系的费米能相应增大,且在低温区费米能随着温度的升高而增大比较缓慢,而在高温区费米能随着温度的升高而增大较快。     

点杂质和Anderson无序对于具有S波配对势的石墨烯性质的影响

基于BCS理论,在紧束缚近似下,通过求解Bogoliubov- de Gennes (BdG)方程,自洽地计算了石墨烯晶格中S波超导配对势对化学势的依赖关系.并分别讨论了点杂质和Anderson无序对体系S波超导配对势的影响.