双因素方差分析模型在霍尔测量中的应用

在测量半导体材料的霍尔效应实验中,研究霍尔电压在不同温度和不同磁场强度下变化情况。文章通过建立双因素方差分析数学模型对实验数据进行分析,判断不同的实验条件对实验结果是否有显著影响。     

Electron spin transitions in quantum Hall systems

A system of two-dimensional electron gas in a strong magnetic field exhibits a remarkable phenomenon known as the fractional quantum Hall effect. Rapid advances in experimental techniques and intense theoretical work for well over a decade have significantly contributed to our understanding of the mechanism behind the effect. It is now a well established fact that electron correlations are largely responsible for the occurrence of this phenomenon. In recent years, theoretical and experimental investigations have revealed that those electron correlations, which are responsible for the quantum Hall effect, are also the reason for various spin transitions in the system. In this review, we systematically follow the theoretical studies of the role spin degree of freedom play in the quantum Hall effect regime and also describe several ingenious experiments reported in recent years which are in good agreement with the emerging theoretical picture.     

Transport processes in magnetically confined plasmas in the nonlinear regime

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.     

Charge dynamics,Majorana condition and the topology of the interacting electromagnetic field

In previous works [1, 2], the 2-dimensional charge transport with parallel (in plane) magnetic field was considered from the theoretical point of view showing explicitly that the specific form of the emergent equation enforces the respective field solution to fulfil the Majorana condition. In this paper we review, explain and analyze these important results in the context of the generated physical effects, namely, the quantum ring as spin filter, the quantum Hall effect and a new one of pure topological origin (as the described by the Aharonov–Casher theorems). The link with supersymmetrical models is briefly discussed.     

Spin hall effect associated with SU(2) gauge field

In this paper, we focus on the connection between spin Hall effect and spin force. Here we investigate that the spin force due to spin-orbit coupling, which, in two-dimensional system, is equivalent to forces of Hirsch and Chudnovsky besides constant factors 3 and $\frac{3}{2}$ respectively, is a part of classic Anandan force, and that the spin Hall effect is an anomalous Hall effect. Furthermore, we develop the method of AC phase to derive the expression for the spin force, and note that the most basic spin Hall effect indeed originate from the AC phase and is therefore an intrinsic quantum mechanical property of spin. This method differs from approach of Berry phase in the study of anomalous Hall effect , which is the intrinsic property of the perfect crystal. On the other hand, we use an elegant skill to show that the Chudnovsky-Drude model is reasonable. Here we have improved the theoretical values of spin Hall conductivity of Chudnovsky. Compared to the theoretical values of spin Hall conductivity in the Chudnovsky-Drude model, ours are in better agreement with experimentation. Finally, we discuss the relation between spin Hall effect and fractional statistics.     

声光效应实验的理论研究和曲线模拟

本文在已有的实验原理的基础上对实验中所涉及的知识作进一步的介绍,对声光效应的过程作进一步的分析,对实验中数据的测量作相应的讨论,并在实验原理的基础上利用mathematica软件作实验数据曲线的理论模拟,从而为声光效应实验提供更完备的理论参考。     

Theory of the phonon Hall effect in paramagnetic dielectrics

Based upon Raman spin-lattice interaction, we propose a theoretical model for the phonon Hall effect in paramagnetic dielectrics, which was discovered recently in an experiment [C. Strohm, G. L. J. A. Rikken, and P. Wyder, Phys. Rev. Lett. 95, 155901 (2005).]. The phonon Hall effect is revealed to be a phonon analogue to the anomalous Hall effect in electron systems. The thermal Hall conductivity is calculated by using the Kubo formula. Our theory reproduces the essential experimental features of the phonon Hall effect, including the sign, magnitude, and linear magnetic field dependence of the thermal Hall conductivity.     

光自旋霍尔效应中的交叉偏振特性研究

从光束角谱理论出发建立了描述光自旋霍尔效应的傍轴传输模型, 利用这一模型分析了光自旋霍尔效应中的交叉偏振特性. 通过分析交叉偏振效应强度和入射角变化的规律, 发现交叉偏振效应越强, 光自旋霍尔效应中的自旋分裂越大. 为便于实验观察, 将入射角选在光自旋霍尔效应较强的布儒斯特角附近, 观测到了强的交叉偏振效应. 增大交叉偏振分量的同时减小初始偏振分量, 可显著增强光自旋霍尔效应. 这一调控方法为研制基于光自旋霍尔效应的新型光子器件提供了理论基础.     

磁性液体的介电特性

在外加磁化场的作用下,磁性液体的介电特性表现出与一般物质所不同的新效应——磁电方向效应,即介电常数不但依赖于外加磁化场的大小,而且还依赖于外加磁化场与电场之间的相对方向。根据实验观察到的磁性液体中的磁性颗粒呈球形,在外加磁化场的作用下,磁性颗粒呈长链形分布的这一实验事实,我们用长链模型进行理论分析,合理地解释了磁电方向效应。理论与实验结果符合。 关键词：     

Screening model of magnetotransport hysteresis observed in bilayer quantum Hall systems

We report on theoretical and experimental investigations of a novel hysteresis effect that has been observed on the magnetoresistance of quantum Hall bilayer systems. Extending to these system a recent approach, based on the Thomas–Fermi–Poisson nonlinear screening theory and a local conductivity model, we are able to explain the hysteresis as being due to screening effects such as the formation of “incompressible strips”, which hinder the electron density in a layer within the quantum Hall regime to reach its equilibrium distribution.     

The dip effect under integer quantized Hall conditions

In this work we investigate an unusual transport phenomenon observed in two-dimensional electron gas under integer quantum Hall effect conditions. Our calculations are based on the screening theory, using a semi-analytical model. The transport anomalies are dip and overshoot effects, where the Hall resistance decreases (or increases) unexpectedly at the quantized resistance plateaus intervals. We report on our numerical findings of the dip effect in the Hall resistance, considering GaAs/AlGaAs heterostructures in which we investigated the effect under different experimental conditions. We show that, similar to overshoot, the amplitude of the dip effect is strongly influenced by the edge reconstruction due to electrostatics. It is observed that the steep potential variation close to the physical boundaries of the sample results in narrower incompressible strips, hence, the experimental observation of the dip effect is limited by the properties of these current carrying strips. By performing standard Hall resistance measurements on gate defined narrow samples, we demonstrate that the predictions of the screening theory is in well agreement with our experimental findings.     

Quantum anomalous Hall effect in real materials

Under a strong magnetic field,the quantum Hall(QH) effect can be observed in two-dimensional electronic gas systems.If the quantized Hall conductivity is acquired in a system without the need of an external magnetic field,then it will give rise to a new quantum state,the quantum anomalous Hall(QAH) state.The QAH state is a novel quantum state that is insulating in the bulk but exhibits unique conducting edge states topologically protected from backscattering and holds great potential for applications in low-power-consumption electronics.The realization of the QAH effect in real materials is of great significance.In this paper,we systematically review the theoretical proposals that have been brought forward to realize the QAH effect in various real material systems or structures,including magnetically doped topological insulators,graphene-based systems,silicene-based systems,two-dimensional organometallic frameworks,quantum wells,and functionalized Sb(111) monolayers,etc.Our paper can help our readers to quickly grasp the recent developments in this field.     

高超声速飞行器磁控热防护霍尔电场数值方法研究

作为一种新概念高超声速热防护手段,磁控热防护系统在实际应用中往往需要考虑霍尔效应的影响.为了在真实气体环境下求解霍尔电场,采用交替隐式近似因子分解法建立并验证了热化学非平衡流体域电场数值求解方法.分析了电场虚拟步进因子和收敛性的关系以及影响步进因子取值的因素,提出了当地变步进因子加速电场收敛方法.研究表明,存在一个最优的步进因子a_p使得霍尔电场收敛速度最快,并且随网格尺度的减小和霍尔系数的增加,最优步进因子a_p变大,电势场收敛速率变慢.对于局部加密网格而言,当地变步进因子法的电势收敛性明显优于常规的定步进因子法.     

Presence of nonlinear interference effects as a source of low frequency excitation force in vibro-acoustography

The vibro-acoustography imaging method consists of forming an image of the deformability of a tissue submitted to a low frequency fLF stress field. This sound field can be created locally by means of a focused annular array emitting two primary beams driven at two close frequencies fa and fb = fa + fLF. In the existing literature, the origin of this stress field has been identified as the low frequency radiation pressure of the two primary beams. However, this work intends to show that another contribution to this internal stress is the low frequency field distributed in the object volume and created by the nonlinear interferences of the two primary beams. This nonlinear field was calculated in the case of multiple ring annular arrays and compared with the qLF beam experimentally measured in a water tank. The agreement between the theoretical and experimental curves provides information on the possibility that this nonlinear effect takes place in vibro-acoustography.     

半导体中自旋轨道耦合及自旋霍尔效应

本文主要评述和介绍半导体微结构中自旋轨道耦合的研究和最近的研究进展。我们细致地讨论了半导体微结构中自旋轨道耦合的物理起源和窄带隙半导体量子阱中的自旋霍尔效应。我们发现目前国际上广泛采用的线性Rashba模型在较大的电子平面波矢处失效:即自旋轨道耦合导致的能带自旋劈裂不再随电子波矢的增加而增加,而是开始下降,即出现强烈的非线性行为。这种非线性的行为起源于导带和价带间耦合的减弱。这种非线性行为还会导致电子的D’yakonov-Perel’自旋弛豫速率在较高能量处下降,与线性模型的结果完全相反。在此基础上,我们构造统一描述电子和空穴自旋霍尔效应的理论框架。我们的方法可以非微扰地计入自旋轨道耦合对本征自旋霍尔效应的影响。我们将此方法应用于强自旋轨道耦合的情形,即窄带隙CdHgTe/CdTe半导体量子阱。我们发现调节外电场或量子阱的阱宽可以作为导致量子相变和本征自旋霍尔效应的开关。我们的工作可能会为区别和实验验证本征自旋霍尔效应提供物理基础。     

The Hall effect and oscillating decay of a magnetic field

The decay of a strong magnetic field in a conducting matter is considered. It is shown that nondissipative Hall currents can considerably change the behavior of the field when it decays. The nonlinear character of the Hall effect leads to the generation of fields of high multipolarity even for most simple initial magnetic configurations. In particular, the evolution of an initially dipole configuration may give rise not only to quadrupole or higher poloidal harmonics but also to a toroidal field that is other than zero only inside the conductor. The nonlinear Hall currents relate different harmonics to each other and, in a sufficiently strong field, may provide efficient energy exchange between them. Due to this redistribution of the magnetic energy, the evolution of different harmonics has an oscillating character. The oscillation period is determined by the characteristic time of Hall drift and may be fairly short in strong magnetic fields.     

Multiscale analysis in nonlinear thermal diffusion problems in composite structures

The aim of this paper is to analyze the asymptotic behavior of the solution of a nonlinear problem arising in the modelling of thermal diffusion in a two-component composite material. We consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We assume that we have nonlinear sources and that at the interface between the two materials the flux is continuous and depends in a dynamical nonlinear way on the jump of the temperature field. We shall be interested in describing the asymptotic behavior of the temperature field in the periodic composite as the small parameter which characterizes the sizes of our two regions tends to zero. We prove that the effective behavior of the solution of this system is governed by a new system, similar to Barenblatt’s model, with additional terms capturing the effect of the interfacial barrier, of the dynamical boundary condition, and of the nonlinear sources.     

基于Pancharatnam-Berry相位和动力学相位调控纵向光子自旋霍尔效应

提出了一种基于Pancharatnam-Berry相位和动力学相位操控纵向光子自旋霍尔效应的方法.理论分析表明:当光场通过一个由Pancharatnam-Berry相位透镜和动力学相位透镜构成的透镜组时,透镜组会存在两个自旋相关的焦点.首先,当左旋和右旋圆偏振光通过微结构相位延迟为π的Pancharatnam-Berry相位透镜时,由于Pancharatnam-Berry相位的自旋相关性,两个圆偏振分量会获得符号相反的Pancharatnam-Berry相位而导致其中一个被聚焦而另一个发散.然后,在Pancharatnam-Berry相位透镜后再插入普通透镜引入动力学相位调制,由于动力学相位是自旋无关,使得这一透镜组,可以在合适的条件下使不同自旋态的光子分别聚焦于纵向上不同焦点处.纵向自旋分裂由两透镜焦距及间距共同决定,因此可以通过改变两个透镜的焦距及其间距获得任意的纵向自旋分裂值.最后,搭建了一套实验装置,所得实验结果与理论结果一致.