A brief review of thermal transport in mesoscopic systems from nonequilibrium Green’s function approach

With the rapidly increasing integration density and power density in nanoscale electronic devices, the thermal management concerning heat generation and energy harvesting becomes quite crucial. Since phonon is the major heat carrier in semiconductors, thermal transport due to phonons in mesoscopic systems has attracted much attention. In quantum transport studies, the nonequilibrium Green’s function (NEGF) method is a versatile and powerful tool that has been developed for several decades. In this review, we will discuss theoretical investigations of thermal transport using the NEGF approach from two aspects. For the aspect of phonon transport, the phonon NEGF method is briefly introduced and its applications on thermal transport in mesoscopic systems including one-dimensional atomic chains, multi-terminal systems, and transient phonon transport are discussed. For the aspect of thermoelectric transport, the caloritronic effects in which the charge, spin, and valley degrees of freedom are manipulated by the temperature gradient are discussed. The time-dependent thermoelectric behavior is also presented in the transient regime within the partitioned scheme based on the NEGF method.     

低维纳米材料量子热输运与自旋热电性质 ——非平衡格林函数方法的应用

低维材料不断涌现的新奇性质吸引着科学研究者的目光. 除了电子的量子输运行为之外, 人们也陆续发现和确认了热输运中显著的量子行为, 如 热导低温量子化、声子子带、尺寸效应、瓶颈效应等. 这些小尺度体系的热输运性质可以很好地用非平衡格林函数来描述. 本文首先介绍了量子热输运的特性、声子非平衡格林函数方法及其在低维纳米材料中的研究进展; 其次回顾了近年来在 一系列低维材料中发现的热-自旋输运现象. 这些自旋热学现象展现了全新的热电转换机制, 有助于设计新型的热电转换器件, 同时也给出了用热产生自旋流的新途径; 最后介绍了线性响应理论以及在此理论框架下结合声子、电子非平衡格林函数方法进行的一些有益的探索. 量子热输运的研究对热效应基础研究以及声子学器件、能量转换器件的发展有着不可替代的重要作用.     

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at \(\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)\) in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.     

Time-dependent density functional theory for quantum transport

The rapid miniaturization of electronic devices motivates research interests in quantum transport. Recently time-dependent quantum transport has become an important research topic. Here we review recent progresses in the development of time-dependent density-functional theory for quantum transport including the theoretical foundation and numerical algorithms. In particular, the reducedsingle electron density matrix based hierarchical equation of motion, which can be derived from Liouville–von Neumann equation, is reviewed in details. The numerical implementation is discussed and simulation results of realistic devices will be given.     

聚噻吩单链量子热输运的第一性原理研究

聚噻吩块体通常被视为绝热材料,其热导率小于1W·m~(-1)·K~(-1).但近年发现对于室温下沿聚噻吩分子链方向排列的无定形聚噻吩纳米纤维,其热导率高于聚噻吩块体,可达4.4W·m~(-1)·K~(-1).为了相对准确地揭示纳米尺度聚噻吩单链热输运的微观特征,从量子力学出发,在密度泛函理论计算的基础上,应用中间插入延展方法结合非平衡格林函数方法,对长度为25.107nm、包含448个原子的聚噻吩单链的量子热输运及其同位素效应进行了研究,并与分子动力学方法模拟的结果进行了详细比较.结果表明:室温下32 nm长的纯聚噻吩单链热导率上限高达30.2 W·m~(-1)·K~(-1),与铅的热导率35 W·m~(-1).K~(-1)相近;相同掺杂比例(原子百分数)下C元素热导的同位素效应比S元素显著;室温下聚噻吩单链中~(12)C,~(13)C等比例随机掺杂时的同位素效应最为显著,此时聚噻吩单链的平均热导至少降低了30%;室温下纯聚噻吩单链的热导随C的相对原子质量增加近似呈反比例减小,随S的相对原子质量增加呈非线性单调增加.该研究对认识和调控聚噻吩这种新型功能材料的热输运特性具有积极的价值.     

两端线型双量子点分子Aharonov-Bohm干涉仪电输运

设计一个两端线型双量子点分子Aharonov-Bohm (A-B)干涉仪. 采用非平衡格林函数技术, 理论研究无含时外场作用下的体系电导和引入含时外场作用下的体系平均电流. 在不考虑含时外场时, 调节点间耦合强度或磁通可以诱导电导共振峰劈裂. 控制穿过A-B干涉仪磁通的有无, 实现了共振峰电导数值在0与1之间的数字转换, 为制造量子开关提供了一个新的物理方案. 同时借助磁通和Rashba自旋轨道相互作用, 获得了自旋过滤. 当体系引入含时外场时, 平均电流曲线展示了旁带效应. 改变含时外场的振幅, 实现了体系平均电流的大小与位置的有效控制, 而调节含时外场的频率, 则可以实现平均电流峰与谷之间的可逆转换. 通过调节磁通与Rashba自旋轨道相互作用, 与自旋相关的平均电流亦得到有效控制. 研究结果为开发利用耦合多量子点链嵌入A-B 干涉仪体系电输运性质提供了新的认知. 上述结果可望对未来的量子器件设计与量子计算发挥重要的指导作用.     

Inelastic low-temperature transport through a quantum dot with a Mn ion

Using the nonequilibrium Hubbard operator Green's function technique, we study the inelastic low-temperature quantum transport through an artificial single-molecule magnet coupled to a single phonon mode. For a minimal model based on CdTe quantum dot doped with a single Mn²⁺ ion (S=5/2), the calculated results show that in the presence of hole–phonon coupling, in addition to main Kondo-like peaks associated with (2S+1) sublevels of spin pair states, satellite Kondo-like peaks originating from emitting phonons appear in the local density of states and differential conductance. Moreover, the number of these phonon-induced Kondo-like peaks depends on the parity of the local large spin, i.e., S=integer or half-integer. It is expected that the intrinsic properties of artificial single-molecule magnets can be obtained by detecting these transport characteristics.     

基于符号函数的注入反馈式蔡氏电路同步控制

蔡氏电路的状态变量不易引出,一般的同步控制方法难以硬件电路实现.针对此类含有电感、电容储能元件的混沌电路,提出一种注入反馈式混沌同步电路设计方法,通过引出状态变量,并在状态变量微分量未知的情况下对系统实施混沌控制.利用该方法,对运动行为不同的两个蔡氏系统,实现了基于符号函数的非线性投影同步控制研究,电路实验结果验证了该方法的可行性和有效性.     

Quantum transport through a Z-shaped silicene nanoribbon

In this work,the electronic transport properties of Z-shaped silicene nanoribbon(ZsSiNR) structure are investigated.The calculations are based on the tight-binding model and Green's function method in Landauer-Biittiker formalism,in which the electronic density of states(DOS),transmission probability,and current-voltage characteristics of the system are calculated,numerically.It is shown that the geometry of the ZsSiNR structure can play an important role to control the electron transport through the system.It is observed that the intensity of electron localization at the edges of the ZsSiNR decreases with the increase of the spin-orbit interaction(SOI) strength.Also,the semiconductor to metallic transition occurs by increasing the SOI strength.The present theoretical results may be useful to design silicene-based devices in nanoelectronics.     

平行耦合双量子点分子A-B干涉仪的电荷及其自旋输运

利用非平衡格林函数方法,理论研究每臂中嵌有一个平行耦合双量子点分子的A-B干涉仪(平行耦合双量子点分子A-B干涉仪)的电荷及其自旋输运性质.无外磁场时,与每臂中嵌有一个量子点的A-B干涉仪相比较,平行耦合双量子点分子A-B干涉仪中电子隧穿变得更加容易发生.当平行耦合双量子点分子A-B干涉仪中引入外磁场时,能够在电导能谱中观察到一个Fano共振和一个反共振,这两种输运状态在磁场取适当数值时能够同时消失.此外,通过调节左右两电极间的偏压、磁通和Rashba自旋轨道相互作用,可以对体系自旋输运进行调控.     

Degradation of Grover’s search under collective phase flips in queries to the oracle

We address the case in which querying the oracle in Grover’s algorithm is exposed to noise including phase distortions. The oracle-box wires can be altered by an opposing party that tries to prevent reception of correct data from the oracle. This situation reflects an experienced truth that any access to prophetic knowledge cannot be common and direct. To study this problem, we introduce a simple model of collective phase distortions on the basis of a phase-damping channel. In the model, the probability of success is not altered via the oracle-box wires per se. Phase distortions of the considered type can hardly be detected via any one-time query to the oracle. However, the probability of success is significantly changed when such errors are introduced as an intermediate step in the Grover iteration. We investigate the probability of success with respect to variations of the parameter that characterizes the amount of phase errors. It turns out that the probability of success decreases significantly even if the error is not very high. Moreover, this probability quickly reduces to the value of one half, which corresponds to the completely mixed state. We also study trade-off relations between quantum coherence and the probability of success in the presence of noise of the considered type.     

Electron transport for a laser-irradiated quantum channel with Rashba spin--orbit coupling

We investigate theoretically the electron transport for a two-level quantum channel (wire) with Rashba spin--orbit coupling under the irradiation of a longitudinally-polarized external laser field at low temperatures. Using the method of equation of motion for Keldysh nonequilibrium Green function, we examine the time-averaged spin polarized conductance for the system with photon polarization parallel to the wire direction. By analytical analysis and a few numerical examples, the interplay effects of the external laser field and the Rashba spin--orbit coupling on the spin-polarized conductance for the system are demonstrated and discussed. It is found that the longitudinally-polarized laser field can adjust the spin polarization rate and produce some photon sideband resonances of the conductance for the system.     

Unsupervised neural networks for solving Troesch’s problem

In this study, stochastic computational intelligence techniques are presented for the solution of Troesch’s boundary value problem. The proposed stochastic solvers use the competency of a feed-forward artificial neural network for mathematical modeling of the problem in an unsupervised manner, whereas the learning of unknown parameters is made with local and global optimization methods as well as their combinations. Genetic algorithm(GA) and pattern search(PS) techniques are used as the global search methods and the interior point method(IPM) is used for an efficient local search. The combination of techniques like GA hybridized with IPM(GA-IPM) and PS hybridized with IPM(PS-IPM) are also applied to solve different forms of the equation. A comparison of the proposed results obtained from GA, PS, IPM, PS-IPM and GA-IPM has been made with the standard solutions including well known analytic techniques of the Adomian decomposition method, the variational iterational method and the homotopy perturbation method. The reliability and effectiveness of the proposed schemes, in term of accuracy and convergence, are evaluated from the results of statistical analysis based on sufficiently large independent runs.     

Application of real space Kerker method in simulating gate-all-around nanowire transistors with realistic discrete dopants

We adopt a self-consistent real space Kerker method to prevent the divergence from charge sloshing in the simulating transistors with realistic discrete dopants in the source and drain regions. The method achieves efficient convergence by avoiding unrealistic long range charge sloshing but keeping effects from short range charge sloshing. Numerical results show that discrete dopants in the source and drain regions could have a bigger influence on the electrical variability than the usual continuous doping without considering charge sloshing. Few discrete dopants and the narrow geometry create a situation with short range Coulomb screening and oscillations of charge density in real space. The dopants induced quasilocalized defect modes in the source region experience short range oscillations in order to reach the drain end of the device.The charging of the defect modes and the oscillations of the charge density are identified by the simulation of the electron density.     

Green's function approach to the impurity state in the Lieb lattice

Wavefunction of an impurity attached to the Lieb lattice is considered by directly computing the Green's function (GF) for the nearest-neighbor tight-binding model. By replacing the lattice GF with a GF array including all the nine GFs defining on the three-atom unit cell of the Lieb lattice, an accurate and efficient numerical technique is developed. Agreement of both the real and imaginary components of the GF between numerical simulation of the lattice GF and continuum-space Fourier transformation is achieved in the whole resonant-energy range. Both results demonstrate that the wavefunction amplitude decays in a power-law pattern while the resonant energy is small and it decays in a pattern stronger than the power law and weaker than exponentially while the resonant energy is large. The decaying exponents depend on the adatom type and location in the unit cell, which directly modifies the temperature-dependent conductance under the variable-range hopping theory.     

Effect of boundary treatments on quantum transport current in the Green’s function and Wigner distribution methods for a nano-scale DG-MOSFET

In this paper, we conduct a study of quantum transport models for a two-dimensional nano-size double gate (DG) MOSFET using two approaches: non-equilibrium Green’s function (NEGF) and Wigner distribution. Both methods are implemented in the framework of the mode space methodology where the electron confinements below the gates are pre-calculated to produce subbands along the vertical direction of the device while the transport along the horizontal channel direction is described by either approach. Each approach handles the open quantum system along the transport direction in a different manner. The NEGF treats the open boundaries with boundary self-energy defined by a Dirichlet to Neumann mapping, which ensures non-reflection at the device boundaries for electron waves leaving the quantum device active region. On the other hand, the Wigner equation method imposes an inflow boundary treatment for the Wigner distribution, which in contrast ensures non-reflection at the boundaries for free electron waves entering the device active region. In both cases the space-charge effect is accounted for by a self-consistent coupling with a Poisson equation. Our goals are to study how the device boundaries are treated in both transport models affects the current calculations, and to investigate the performance of both approaches in modeling the DG-MOSFET. Numerical results show mostly consistent quantum transport characteristics of the DG-MOSFET using both methods, though with higher transport current for the Wigner equation method, and also provide the current–voltage (I–V) curve dependence on various physical parameters such as the gate voltage and the oxide thickness.     

热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性与守恒量

研究了变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性和守恒量.在群的无限小变换下,定义了变质量Chetaev型非完整系统Appell方程Mei对称性和共形不变性,给出了该系统Mei对称性的共形不变性确定方程,并推导出系统相应的守恒量表达式.最后,给出了应用算例.     

Working Memory Decline in Alzheimer’s Disease Is Detected by Complexity Analysis of Multimodal EEG-fNIRS

Alzheimer’s disease (AD) is characterized by working memory (WM) failures that can be assessed at early stages through administering clinical tests. Ecological neuroimaging, such as Electroencephalography (EEG) and functional Near Infrared Spectroscopy (fNIRS), may be employed during these tests to support AD early diagnosis within clinical settings. Multimodal EEG-fNIRS could measure brain activity along with neurovascular coupling (NC) and detect their modifications associated with AD. Data analysis procedures based on signal complexity are suitable to estimate electrical and hemodynamic brain activity or their mutual information (NC) during non-structured experimental paradigms. In this study, sample entropy of whole-head EEG and frontal/prefrontal cortex fNIRS was evaluated to assess brain activity in early AD and healthy controls (HC) during WM tasks (i.e., Rey–Osterrieth complex figure and Raven’s progressive matrices). Moreover, conditional entropy between EEG and fNIRS was evaluated as indicative of NC. The findings demonstrated the capability of complexity analysis of multimodal EEG-fNIRS to detect WM decline in AD. Furthermore, a multivariate data-driven analysis, performed on these entropy metrics and based on the General Linear Model, allowed classifying AD and HC with an AUC up to 0.88. EEG-fNIRS may represent a powerful tool for the clinical evaluation of WM decline in early AD.     

An analytic and numerical solution with spectral Green's function method for transport equation in spherical geometry

Since in many cases curvilinear geometry is more appropriate than cartesian geometry for precise modeling of the complex systems for reactor calculation, we have developed the spectral Green's function (SGF) method which is employed to obtain angular and scalar flux distributions in heterogeneous sphere geometry with isotropic scattering. In this study, we showed that the neutron transport problems of homogeneous spheres could be reduced to the solution of plane geometry equation.Finally, some results are discussed and compared with those already obtained by diamond difference scheme to test the accuracy of the results. The agreement is satisfactory. SGF method is very suitable for the numerical solution of the neutron transport equation with isotropic scattering.