光自旋霍尔效应及其研究进展

光束在经过非均匀介质后,自旋角动量相反(左、右旋圆偏振)的光子在垂直于入射面的横向相互分离,造成光束的自旋分裂,这种现象叫做光自旋霍尔效应.它类似于电子系统中的自旋霍尔效应:自旋光子扮演自旋电子的角色,而折射率梯度则起外场作用.光自旋霍尔效应为操控光子提供了新的途径,在纳米光学、量子信息和半导体物理方面具有重要的应用前景;同时由于它与凝聚态和高能物理中的带电粒子自旋霍尔效应有高度的相似性和共同的拓扑根源,所以又为测量自旋霍尔效应这类弱拓扑现象提供了独特而又方便的机会.文章简单介绍了光自旋霍尔效应,并总结了近几年国内外的研究进展.     

量子霍尔效应

从经典的霍尔效应开始,比较系统地、深入浅出地介绍了量子霍尔效应及其所涉及的一些新概念和实际应用。     

磁性拓扑绝缘体中的量子化反常霍尔效应

文章从平常霍尔效应出发,介绍了反常霍尔效应及其内秉物理机制,并在此基础上介绍了其量子化版本——量子化反常霍尔效应.然后从拓扑有序态的角度,重点讨论了量子化反常霍尔效应与量子霍尔效应、量子自旋霍尔效应、拓扑绝缘体等之间的区别与内在联系.最后介绍了通过在拓扑绝缘体（Bi2Se3, Bi2Te3 和 Sb2Te3）薄膜中掺杂过渡金属元素（Cr 或 Fe）实现量子化反常霍尔效应的方法.     

Insensitivity of Quantized Hall Conductance to Disorder and Interactions

A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron–electron interactions. We assume that there exists a nonzero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we prove that the Hall conductance _xy and the diagonal conductance _yy satisfy | _xy+e ² /h|const·L ^–1/2 and | _yy|const·L ^–1/12. Here e ²/h is the universal conductance with the charge –e of the electron and the Planck constant h; is the filling factor of the Landau level; and L is the linear dimension of the system. In the thermodynamic limit, our results show _xy=–e ² /h and _yy=0. The former implies that integral and fractional filling factors with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.     

折射率梯度引起反转的光自旋霍尔效应研究

从经典电动力学出发,研究了由折射率梯度导致的反转光自旋霍尔效应。通过分析光从光疏介质入射到光密介质和从光密介质入射到光疏介质两种情况,揭示了光自旋霍尔效应中的横移与偏振态、折射率梯度以及入射角等因素的定性关系。当入射角一定时,光从光疏介质入射到光密介质时的水平偏振横移绝对值大于垂直偏振横移,而从光密介质入射到光疏介质的情况正好与之相反,并且传输场的横移方向取决于折射率梯度方向,增大入射角能明显增强光自旋霍尔效应,对某一特定的线偏振光束,其左、右旋圆偏振光分量的横移等值反向。这些研究结果为调控光自旋霍尔效应提供了有效途径。     

Quantum Hall skyrmions with higher topological charge

We have investigated quantum Hall skyrmions with more than one unit of topological, and hence electric, charge. Using a combination of analytic and numerical methods we find the counterintuitive result that when the Zeeman energy is tuned to values much smaller than the interaction energy ( ), the creation energy of a charge two skyrmion becomes less than twice the creation energy of a charge one skyrmion, i.e. skyrmions bind in pairs. The doubly charged skyrmions are stable to further accretion of charge and exhibit a larger spin per unit charge than charge one skyrmions which would, in principle, signal this pairing. 1997 Elsevier Science B.V. All rights reserved.     

转换反射中光自旋霍尔效应的自旋堆积方向

从理论上和实验上研究了转换反射中光自旋霍尔效应的自旋堆积方向的方法,建立了描述光束在空气-棱镜界面反射的自旋堆积模型,揭示了横移与光束入射偏振角的定性关系。研究发现,当入射角小于布儒斯特角时,随着入射偏振角的逐渐增大,自旋堆积的方向发生反转。而当入射角大于布儒斯特角时,自旋堆积的方向不再随入射偏振角的变化而反转。结果表明,在光束入射角为确定值且小于布儒斯特角的情况下,可以通过调控光束的入射偏振角转换自旋堆积的方向。转换自旋堆积方向的研究为有效调控光自旋霍尔效应提供了新的途径。     

Quantum critical Hall exponents

We investigate a finite size “double scaling” hypothesis using data from an experiment on a quantum Hall system with short range disorder ,  and . For Hall bars of width w at temperature T   the scaling form is w^−μT^−κ$w^{-\mu }{T}^{-\kappa }$, where the critical exponent μ≈0.23$\mu \approx 0.23$ we extract from the data is comparable to the multi-fractal exponent _α0−2${\alpha }_0-2$ obtained from the Chalker–Coddington (CC) model [4]. We also use the data to find the approximate location (in the resistivity plane) of seven quantum critical points, all of which closely agree with the predictions derived long ago from the modular symmetry of a toroidal σ-model with m matter fields [5]. The value _ν8=2.60513…${\nu }_8=2.60513\dots$ of the localisation exponent obtained from the m=8$m=8$ model is in excellent agreement with the best available numerical value _νnum=2.607±0.004${\nu }_{\mathrm{num}}=2.607\pm 0.004$ derived from the CC-model [6]. Existing experimental data appear to favour the m=9$m=9$ model, suggesting that the quantum Hall system is not in the same universality class as the CC-model. We discuss the reason this may not be the case, and propose experimental tests to distinguish between the two possibilities.     

Chaotic Cyclotron and Hall Trajectories Due to Spin-Orbit Coupling

It is demonstrated that the synergistic effect of a gauge field, Rashba spin-orbit coupling (SOC), and Zeeman splitting can generate chaotic cyclotron and Hall trajectories of particles. The physical origin of the chaotic behavior is that the SOC produces a spin-dependent (so-called anomalous) contribution to the particle velocity and the presence of Zeeman field reduces the number of integrals of motion. By using analytical and numerical arguments, the conditions of chaos emergence are studied and the dynamics both in the regular and chaotic regimes is reported. The critical dependence of the dynamic patterns (such as the chaotic regime onset) on small variations in the initial conditions and problem parameters, that is the SOC and/or Zeeman constants, is observed. The transition to chaotic regime is further verified by the analysis of phase portraits as well as Lyapunov exponents spectrum. The considered chaotic behavior can occur in solid state systems, weakly relativistic plasmas, and cold atomic gases with synthetic gauge fields and spin-related couplings.     

超构材料中的光学量子自旋霍尔效应

电子的量子自旋霍尔效应的发现推进了当今凝聚态物理学的发展,它是一种电子自旋依赖的具有量子行为的输运效应.近年来,大量的理论和实验研究表明,描述电磁波场运动规律的麦克斯韦方程组内禀了光的量子自旋霍尔效应,存在于界面的倏逝波表现出强烈的自旋与动量关联性.得益于新兴的光学材料:超构材料(metamaterials)的发展,不仅能够任意设定光学参数,同时也能引入很多复杂的自旋-轨道耦合机理,让我们能够更加清晰地了解和验证其中的物理机理.本文对超构材料中量子自旋霍尔效应做了简要的介绍,内容主要包括真空中光的量子自旋霍尔效应的物理本质、电单负和磁单负超构材料能带反转导致的不同拓扑相的界面态、拓扑电路系统中光量子自旋霍尔效应等.     

Quantum Monty Hall Problem under Decoherence

We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing, and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in case of depolarizing channel for Alice＇s quantum strategy. Whereas in case of dephasing noise, the game is not influenced by the quantum channel. For amplitude damping channel, Bob＇s payoffs are found symmetrical about a decoherence of 50% and the maximum occurs at this value of decoherence for his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob＇s classical strategy remains always dominant against any choice of Alice＇s strategy.     

Quantum Monty Hall Problem under Decoherence

We study the effect of decoherence on quantum Monty Hall problem under theinfluence of amplitude damping, depolarizing, and dephasing channels. It isshown that under the effect of decoherence, there is a Nash equilibrium ofthe game in case of depolarizing channel for Alice's quantum strategy.Whereas in case of dephasing noise, the game is not influenced by thequantum channel. For amplitude damping channel, Bob's payoffs are foundsymmetrical about a decoherence of 50% and the maximum occurs at this value of decoherence for his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob's classical strategy remains always dominant against any choice of Alice's strategy.     

基于霍尔效应的角位移传感器演示仪

应用霍尔效应实现了对角度改变的显示,把一个非电量转换成电量输出,使得容易实现对角度的测量和自动控制。     

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall （QH） effect on a noncommutative phase space （NCPS）. By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and θ^-, respectively. In our calculation, we assume that these parameters vary from laver to laver.     

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall (QH) effect on a noncommutative phase space (NCPS). By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and \bar{θ}, respectively. In our calculation, we assume that these parameters vary from layer to layer.     

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.     

Spectral Gaps of Quantum Hall Systems with Interactions

A two-dimensional quantum Hall system without disorder for a wide class of interactions including any two-body interaction with finite range is studied by using the Lieb–Schultz–Mattis method [Ann. Phys. (N.Y.) 16:407 (1961)]. The model is defined on an infinitely long strip with a fixed, large width, and the Hilbert space is restricted to the lowest (n _max+1) Landau levels with a large integer n _max. We prove that, for a noninteger filling of the Landau levels, either (i) there is a symmetry breaking at zero temperature or (ii) there is only one infinite-volume ground state with a gapless excitation. We also prove the following two theorems: (a) If a pure infinite-volume ground state has a nonzero excitation gap for a noninteger filling , then a translational symmetry breaking occurs at zero temperature. (b) Suppose that there is no non-translationally invariant infinite-volume ground state. Then, if a pure infinite-volume ground state has a nonzero excitation gap, the filling factor must be equal to a rational number. Here the ground state is allowed to have a periodic structure which is a consequence of the translational symmetry breaking. We also discuss the relation between our results and the quantized Hall conductance, and phenomenologically explain why odd denominators of filling fractions giving the quantized Hall conductance are favored exclusively.     

Quantum Version of a Generalized Monty Hall Game and Its Possible Applications to Quantum Secure Communications

In this work, the authors propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free and not fixed on its regular values. The developed quantum scheme is then used to study the expected payoff of the player, using both a separable and an entangled initial‐state. In the two cases, the classical mixed‐strategy payoff is recovered under certain conditions. Lastly, the authors extend the quantum scheme to include multiple independent players, and use this extension to sketch two possible application of the game mechanics to quantum networks, specifically, two validated, multi‐party, key‐distribution quantum protocols.     

声子角动量与手性声子

在经典的物理学理论中,声子广泛地被认为是线极化的、不具有角动量的.最近的理论研究发现,在具有自旋声子相互作用的磁性体系(时间反演对称性破缺)中,声子可以携带非零的角动量,在零温时声子除了具有零点能以外还带有零点角动量;非零的声子角动量将会修正通过爱因斯坦-德哈斯效应测量的回磁比.在非磁性材料中,总的声子角动量为零,但是在空间反演对称性破缺的六角晶格体系中,其倒格子空间的高对称点上声子具有角动量,并具有确定的手性;三重旋转对称操作给予声子量子化的赝角动量,赝角动量的守恒将决定电子谷间散射的选择定则;此外还理论预测了谷声子霍尔效应.