Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

Coherence and Localization in 2D Luttinger Liquids

Recent measurements on the resistivity of (La-Sr)(2)CuO4 are shown to tit within the general framework of Luttinger liquid transport theory. They exhibit a crossover from the spin-charge separated ''holon nondrag regime'' usually observed, with rho(ab) similar to T, to a ''localizing'' regime dominated by impurity scattering at low temperature. The proportionality of rho(c) and rho(ab) and the giant anisotropy follow directly from the theory.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Scattering of carriers by charged dislocations in semiconductors

The scattering of carriers by charged dislocations in semiconductors is studied within the framework of the linearized Boltzmann transport theory with an emphasis on examining consequences of the extreme anisotropy of the cylindrically symmetric scattering potential. A new closed-form approximate expression for the carrier mobility valid for all temperatures is proposed. The ratios of quantum and transport scattering times are evaluated after averaging over the anisotropy in the relaxation time. The value of the Hall scattering factor computed for charged dislocation scattering indicates that there may be a factor of two error in the experimental mobility estimates using the Hall data. An expression for the resistivity tensor when the dislocations are tilted with respect to the plane of transport is derived. Finally, an expression for the isotropic relaxation time is derived when the dislocations are located within the sample with a uniform angular distribution.

Effect of strain on electronic and thermoelectric properties of few layers to bulk MoS2

The sensitive dependence of the electronic and thermoelectric properties of MoS2 on applied strain opens up a variety of applications in the emerging area of straintronics. Using first-principles-based density functional theory calculations, we show that the band gap of a few layers of MoS2 can be tuned by applying normal compressive (NC) strain, biaxial compressive (BC) strain, and biaxial tensile (BT) strain. A reversible semiconductor-to-metal transition (S-M transition) is observed under all three types of strain. In the case of NC strain, the threshold strain at which the S-M transition occurs increases when the number of layers increase and becomes maximum for the bulk. On the other hand, the threshold strain for the S-M transition in both BC and BT strains decreases when the number of layers increase. The difference in the mechanisms for the S-M transition is explained for different types of applied strain. Furthermore, the effect of both strain type and the number of layers on the transport properties are also studied using Botzmann transport theory. We optimize the transport properties as a function of the number of layers and the applied strain. 3L- and 2L-MoS2 emerge as the most efficient thermoelectric materials under NC and BT strain, respectively. The calculated thermopower is large and comparable to some of the best thermoelectric materials. A comparison among the feasibility of these three types of strain is also discussed.

High temperature thermoelectric properties of Zr and Hf based transition metal dichalcogenides: A first principles study

We investigate the electronic and thermal transport properties of bulk MX2 compounds (M = Zr, Hf and X = S, Se) by first-principles calculations and semi-classical Boltzmann transport theory. The band structure shows the confinement of heavy and light bands along the out of plane and in-plane directions, respectively. This results in high electrical conductivity (sigma) and large thermopower leading to a high power factor (S-2 sigma) for moderate n-type doping. The phonon dispersion demonstrates low frequency flat acoustical modes, which results in low group velocities (v(g)). Consequently, lowering the lattice thermal conductivity (kappa(latt)) below 2 W/m K. Low kappa(latt) combined with high power factor results in ZT > 0.8 for all the bulk MX2 compounds at high temperature of 1200 K. In particular, the ZT(max) of HfSe2 exceeds 1 at 1400 K. Our results show that Hf/Zr based dichalcogenides are very promising for high temperature thermoelectric application. (C) 2015 AIP Publishing LLC.

Desenvolvimento de um método espectronodal livre de erros de truncamento espacial para problemas adjuntos de transporte de partículas neutras monoenergéticas na formulação de ordenadas discretas em geometria unidimensional

Um método numérico nodal livre de erros de truncamento espacial é desenvolvido para problemas adjuntos de transporte de partículas neutras monoenergéticas em geometria unidimensional com fonte fixa na formulação de ordenadas discretas (SN). As incógnitas no método são os fluxos angulares adjuntos médios nos nodos e os fluxos angulares adjuntos nas fronteiras dos nodos, e os valores numéricos gerados para essas quantidades são os obtidos a partir da solução analítica das equações SN adjuntas. O método é fundamentado no uso da convencional equação adjunta SN discretizada de balanço espacial, que é válida para cada nodo de discretização espacial e para cada direção discreta da quadratura angular, e de uma equação auxiliar adjunta não convencional, que contém uma função de Green para os fluxos angulares adjuntos médios nos nodos em termos dos fluxos angulares adjuntos emergentes das fronteiras dos nodos e da fonte adjunta interior. Resultados numéricos são fornecidos para ilustrarem a precisão do método proposto.

Aplicações do formalismo de Keldysh ao transporte e ao bombeamento de calor em nanoestruturas

Num regime balísstico e a baixas temperaturas, a fórmula de Landauer dá uma boa descrição do transporte de calor para nano-junções conectadas a dois fios acoplados a banhos térmicos a temperaturas diferentes. Partindo de um modelo microscópico e utilizando o método de funções de Green fora do equilíbrio, é possível obter uma expressão para a condutância térmica na nano-junção equivalente a fórmula de Landauer. Esta depende dos valores das constantes de acoplamento entre os modos de fônons da região central e dos fios, além do gradiente térmico. A expressão para a condutância térmica é muito semelhante aquela obtida para a condutância elétrica. Neste trabalho nós apresentamos o método para o cálculo de grandezas relacionadas ao transporte térmico em um regime onde não há um gradiente de temperatura entre os reservatórios mas o sistema sofre uma perturbação dependente do tempo. Ou seja, com uma escolha conveniente da parametrização temporal dos termos de acoplamento entre a nano-junção e os fios é possível produzir uma corrente de calor na ausência de diferença de temperaturas entre os banhos térmicos aos quais os fios estão conectados. Esse fenômeno caracteriza o bombeamento de calor. Desenvolvemos uma teoria de transporte dependente do tempo para descrever o bombeamento. A teoria é geral, dependendo da densidade de fônons, da intensidade e dependência temporal do acoplamento. Aplicamos o formalismo em um modelo simples demonstrando que, em princípio, é possível bombear calor através de uma cadeia linear de átomos sem gradiente térmico.

Shell effect and capture cross sections in the synthesis of superheavy nuclei

The shell effect is included in the improved isospin dependent quantum molecular dynamics model in which the shell correction energy of the system is calculated by using the deformed two-center shell model. A switch function is introduced to connect the shell correction energy of the projectile and the target with that of the compound nucleus during the dynamical fusion process. It is found that the calculated capture cross sections reproduce the experimental data quantitatively at the energy near the Coulomb barrier. The capture cross sections for reaction (35) (80) Br + (82) (208) Pb -> (117) (288) X are also calculated and discussed.

Guiding of 150 keV O6+ ions through nanocapillaries in an uncoated Al2O3 membrane: special time dependence of the transmission profile width

This paper reports that the transmission of O6+ ions with energy of 150keV through capillaries in an uncoated Al2O3 membrane was measured, and agreements with previously reported results in general angular distribution of the transmitted ions and the transmission fractions as a function of the tilt angle well fitted to Gaussian-like functions were observed. Due to using an uncoated capillary membrane, our c is larger than that using a gold-coated one with a smaller value of E-p/q, which suggests a larger equilibrium charge Q(infinity) in our experiment. The observed special width variation with time and a larger width than that using a smaller E-p/q were qualitatively explained by using mean-field classical transport theory based on a classical-trajectory Monte Carlo simulation.

The neutron/proton ratio of squeezed-out nucleons and the high density behavior of the nuclear symmetry energy

Within a transport model it is shown that the neutron/proton ratio of squeezed-out nucleons perpendicular to the reaction plane, especially at high transverse momenta, in heavy-ion reactions induced by high energy neutron-rich nuclei can be a useful tool for studying the high density behavior of the nuclear symmetry energy.

Production cross sections of superheavy nuclei based on dinuclear system model

The barrier distribution function method is introduced in the dinuclear system model in the calculation of the transmission probability, which is the first stage in the synthesis of superheavy nuclei. Dynamical deformation and averaging collision orientations are considered in the calculation of the fusion probability by solving master equation numerically. Survival probability with respect to xn evaporation channel (x = 1-5) in the de-excitation process of the thermal compound nucleus is calculated, in which the level density of the Fermi-gas model is used. Production cross sections of a series of superheavy nuclei formed in the reactions taken magic and deformed nuclei as target in Ca-48 induced reactions are studied systematically. The calculated results are in good agreement with available experimental data. Isotopic dependence of the production cross sections in the reactions Ca-48 + Pu is analyzed.

基于重离子输运理论对超重核合成及非对称核物质状态方程的研究

本论文基于重离子输运理论模型对当前人们感兴趣的超重核合成及非对称核物质状态方程做了研究。基于双核系统概念建立了一个描述超重核合成的理论模型。这个模型中通过求解Fokker-Planck方程来描述重离子碰撞过程的能量、角动量以及形变等的弛豫过程，从而合理地包含了重离子熔合过程中的动力学效应。在求解弹靶的质量扩散时采用了数值求解主方程的方法，避免对势能面做任何近似，因此能够充分地体现重离子熔合过程中弹靶的结构效应。本文利用这一模型计算了重离子熔合形成超重元素的最佳激发能、熔合几率、复合核的存活几率以及蒸发剩余核截面等，并给出了合成超重核的最佳弹靶组合。计算了超重核形成的最佳激发能，在符合已有最佳激发能实验数据的基础上预言了基于冷熔合反应合成114，116和118号元素的最佳激发能。计算了重离子熔合反应的熔合几率。结果表明，随着反应系统变得越来越重，重离子的熔合几率呈指数规律下降，准裂变变得越来越严重。这解释了实验上观测到的超重剩余核截面随体系的变重而急剧下降的现象。研究了重离子熔合截面的弹靶相关性。结果表明弹靶的质量非对称度越高越有利于熔合生成复合核，同时重离子熔合截面还强烈地依赖于弹靶结构。重离子的熔合过程是合成超重元素的关键因素之一，另一个影响超重核合成的因素是超重复合核的存活几率。基于统计模型，系统的研究了超重复合核存活几率的质量、能量、角动量等相关性。计算了基于冷熔合反应的蒸发剩余截面，得到的结果与实验基本符合，并预言了基于冷熔合反应生成114，116和115号元素的截面。在研究超重核蒸发剩余截面的弹靶相关性的基础上给出了合成超重核的最佳弹靶组合。计算表明，在挑选弹靶组合时使得合成的超重复合核是奇A核则会得到更高的奇数中子蒸发剩余核截面。计算给出了超重复合核的自旋布居及其对裂变位垒和鞍点态形变的依赖性。发现超重复合核的自旋布居强烈地依赖于复合核的裂变位垒，高的裂变位垒会给出宽的自旋布居；而超重复合核的自旋布居对鞍点态形变不是很敏感。另外研究了多核子转移反应合成超重元素的可能性。结果表明基于多核子转移反应合成大于108号的元素是很困难的。非对称核物质状态方程由于其对天体物理及理解奇异核结构的重要性，因此是人们长期以来一直感兴趣的研究内容，然而直到现在人们对核物质状态方程特别是高密核物质和非对称核物质状态状态方程仍了解甚少。基于Skyrme-Hartree-Fock理论以及同位旋相关的量子分子动力学（IQMD）模型研究了非对称核物质的化学不稳定性，结果表明非对称核物质可以发生化学不稳定性，且化学不稳定性发生的条件依赖于单粒子势能的密度相关形式。同时计算表明化学不稳定性是可以发生在真实的重离子碰撞过程中的，且在入射能量较高时化学不稳定性会消失。另外首次研究了高密核物质的化学不稳定性及其发生的条件。由于实验室很难达到很高密度的核物质，而中子星是由致密的极丰中子物质组成，因此提供了研究高密非对称核物质的自然实验室。基于Skyrme-Hartree-Fock理论研究了两种典型的非对称核物质状态方程（软对称势和硬对称势）对中子星中质子百分比的影响。另外研究了热中子星中质子百分比的温度相关性，发现热中子星中质子百分比随温度的升高而减小。基于IQMD模型研究了同位旋相分化现象的产生机制。通过与MSU的实验数据比较指出核物质应该有软的对称势。研究了重离子碰撞过程中的径向流现象，及其同位旋效应。计算了径向流产生的能量闭，并给出了实验上利用径向流产生的能量闭来提取非对称核物质状态方程的方法。

非相对论重离子碰撞动力学的两体关联输运理论

论文系统地介绍和分析了当前几类描述重离子碰撞动力学过程输运理论的优点和缺点，并针对这些理论的不足作为建立我们理论模型的出发点。例如BUU（Boltzmann-Uehling-Uhlenbeck）系列的输运过程，可以通过不同方法从量子多体理论依照扩展的时间相关的Hartree-Fock（ETDHF）的基本思想推导出来，并对重离子碰撞过程中有关平均场物理量给出了合理的描述。但由于推导中采用了一些半经典近似和参数化近似，破坏了平均场合碰撞项之间的动力学自洽耦合。特别是数值计算中采用了实验粒子系综平均法，从而丢失了多体关联和涨落，使其无法直接描述重离子碰撞中基本的碎块形成和多重碎裂过程。而量子分子动力学（QMD）系列的理论能够给出重离子碰撞过程中碎块形成的动力学描述，但至今无法从量子多体理论推导出有关QMD的输运方程。碰撞项是在数值计算中通过Monte Carlo抽样技术人为地加入的。那么，如何从量子多体理论出发推导出描述重离子碰撞动力学过程的，可将时间相关的平均场，多体关联进行自洽耦合描述的量子输运理论就成了本论文工作的中心目的。 基于王顺金等人建立的多体关联动力学理论，选用时间相关的相干态单粒子基矢作为新理论的工作表象，对两体关联动力学中的一体密度矩阵和两体关联函数进行轨道展开，推导出了描述非相对论重离子碰撞动力学过程的两体关联输运理论TBCTT（Two-Body Correlation Transport Theory���。TBCTT是一组包括时间相关的平均场，两体关联和Pauli原理的自洽耦合的动力学方程组。其中时间相关的相干单粒子基矢是该理论的一个关键问题。其时间演化的动力学可由多种不同的方法得到，如时间相关的Hartree-Fock方法，时间相关的变分方法等。但作为建立TBCTT工作的第一步，为了计算简便，我们采用经典的Hamilton方程来描述相干单粒子基矢中相空间参数的时间演化，然后通过与两体关联动力学的耦合而恢复TBCCT基本的量子特征。 利用TBCTT对几组轻的碰撞系统进行了数值计算和分析。计算结果表明：TBCTT可以给出重离子碰撞过程中的有关物理量时间演化过程的合理描述，得到了在不同入射道条件下与QMD模型的可比性结果。同时也在组态空间的有限截断和两体关联函数不同的等级截断下均得到了碰撞系统总动量，总能量和总粒子数的近似守恒结果，特别是能量守恒，这是一般半经典输运理论中一个重要的困难问题。另外还得到了两体关联函数不同的等级截断近似对碰撞动力学方面不同的描述。所用这些数值计算结果充分表明：TBCTT是一个有希望和有发展前途的能够描述重离子碰撞动力学的量子输运理论。最后我们对当前计算中所采用的近似和存在的问题进行了分析和讨论，提出了进一步改进和完善TBCTT的途径和方案。 我们在开始TBCTT的研究之前还对QMD进行了仔细的研究和改进。通过在平均场中引入Pauli势和对称势并利用摩擦冷却方法构造原子核基态，得到了一种改进的量子分子动力学MQMD。利用这种MQMD研究了12C+12C反应多重碎裂过程中的核结构效应，得到了与AMD和实验数据基本一致的结果。对QMD的改进和应用为开展TBCTT的研究工作创造了必要条件和准备。