Arithmetic of the Integer Quantum Hall Effect

The integer quantum Hall effect (IQHE) is analysed, considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted, and their variation is studied as a function of magnetic field. The number of current-carrying electrons is found to have a saw-tooth variation with magnetic field. The analysis addresses certain basic questions in the IQHE, particularly the one about floatation of extended states as the magnetic field tends to zero.     

Quantum Hall Effect

The gap equation for the electron self-energyfunction is considered in the framework of (2 +1)-dimensional quantum electrodynamics. The fillingfactor upsilon for the quantum Hall effect is related to a free parameter by considering thedevelopment of the gap equation. The latter is shown tobe expandable in the power series ofm²/p², with p being the modulus ofthe momentum of a single Hall electron and m its physical mass.     

Quantum Hall Effect on the Hyperbolic Plane

In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use the pairing between K-theory and cyclic cohomology theory, to identify this geometric invariant with a topological index, thereby proving the integrality of the Hall conductivity in this case. Received: 17 March 1997 / Accepted: 24 April 1997     

Integer Quantum Hall Effect in a Two-Orbital Square Lattice with Chern Number C=2

We investigate numerically the integer quantum Hall effect in a two-orbital square lattice.The Hall plateauσ_h = 2(e~2/h) is well defined with the Chern number C = ±2.With the increasing disorder,both the Hall plateau and the gap of density of states decrease gradually in width,and finally the gap disappears before vanishing of the Hall plateau.Compared with the Hall plateau induced by the external magnetic field,the one in our system is more robust against disorder.We also find that the transition from the Hall plateau to zero Hall conductance becomes sharper by increasing the size of the system.     

Form of Scaling Function in Quantum Hall Plateau Transitions

We have measured the temperature dependence of the resistance Rxx and Rxy of a two-dimensional electron system in the regime of the quantum Hall plateau transition. We observe for our sample a considerable large critical exponent κ～ 0.66 - 0.77, which may be due to the dominant electron-phonon scattering. Further we find a simple exponential form of Rxx = Rc exp（-s） in agreement with the theoretically proposed universal scaling function.     

Small-Angle Neutron Scattering Wave Interference on Ferromagnetic Alloys

The detection conditions and features of direct and scattered neutron wave interference are studied on magnetized Co₆₇Fe₃₁V₂ alloy slabs. The angular intensity distributions of neutrons passed through a sample are measured for the opposite polarization directions of the initial neutron beam. The sought-for effect that is induced by the magnetic scattering on crystal structure irregularities in specimens manifest itself by different areas of peaks “without neutron spin flip.” The ratio of these areas depends on the thermal treatment mode, sample thickness and strength of the magnetic field applied to the sample. The peaks “with neutron spin flip” are due to the mechanism of neutron wave passage through magnetononcollinear boundaries. The methods for experimental data acquisition and processing are reported as well.     

Small-Angle X-Ray Scattering Study on Nanostructures of Polyimide Films

Inorganic nanohybrid polyimide （PI） is widely applied in electrical and electronic devices for its outstanding insulating properties. Samples IOOCR and IOONH are made in Dupont. Among them, IOONH is a kind of pure PI films; however, IOOCR is a kind of inorganic nanohybrid PI films with excellent corona-resistance. The nanostructure of PI films is investigated with small-angle x-ray scattering technique and transmission electron microscopy （TEM）. The normalized volume fractions of the scatterers in the specimens are obtained with a tangent-by-tangent data analysis for the small-angle x-ray scattering data. The multi-hierarchical scatterers of IOONH can be divided into two dominant components, i.e., the sharp component and the wide component. The sharp component is corresponding to the contribution of PI molecular chains, and the wide component includes the aggregates formed by PI molecular chains and the film has nested dual-fractal characteristics, nevertheless the IOOCR film possesses three types of scale scattering made up of inorganic nanoparticles, molecular chains and aggregates. The present films have multi-fractal structures. The distribution and structure of scattering body of two kinds of PI films are analyzed. The results of SAXS agree well with those of TEM methods.     

Anomalous Anti-Stokes Scattering Signal as an Indicator of Macrofilled Magnetoexciton Levels in the Quantum Hall Effect Regime

JETP Letters - The Raman study of strongly interacting two-dimensional electron systems based on ZnO/MgZnO has revealed an anomalously intense spectral line of the anti-Stokes component of the spin...     

Electric Field Effect on the Fractional Quantum Hall Conductivity

We have studied the effect of an external electric field on the dc fractional quantum Hall conductivity of a two-dimensional system with the dynamic structure function in the single-mode approximation. In analogy with the integral quantum Hall effect and euperconductivity, a gap-dependent critical electric current J_c, also exists in the case of fracctional quantum Hall conduction, above which is the maximum current for system to maintain superfluidity. We also find that, depending on the gap width and the phonon velocity, phonon may or may not contribute to the conductivity even at a finite lattice temperature, in agreement with experiments.     

Electronic Wave-Packets in Integer Quantum Hall Edge Channels: Relaxation and Dissipative Effects

We theoretically investigate the evolution of the peak height of energy-resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor equal to two. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energies. We investigate this quantity assuming a short-range capacitive coupling between the edges. Moreover, we also phenomenologically take into account the possibility of energy dissipation towards additional degrees of freedom—both linear and quadratic—in the injection energy. Through a comparison with recent experimental data, we rule out the non-dissipative case as well as a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate for describing the behavior of the quasi-particle peak at short enough propagation lengths.     

分数量子霍尔效应的新理论

在经典霍尔效应中 ,霍尔电压ＶＨ 线性正比于垂直方向的外场Ｂ⊥ ,并且沿电流方向的纵向电压Ｖ∥ 也随Ｂ⊥ 的增加而连续上升 .1980年 ,冯·克里青 (ＫｌａｕｓｖｏｎＫｌｉｔｚｉｎｇ)用半导体场效应晶体管进行霍尔测量 ,研究被限制在二维平面内的电子运动 .他发现 ,在极低温和强磁场的条件下 ,霍尔电压ＶＨ 不再随外场的增加而线性增加 ,而是 (在ＶＨ-Ｂ⊥ 图上 )表现为一连串ＶＨ =常数的阶跃平台 .与一个个平台相对应的霍尔电阻ＶＨ Ｉ(Ｉ是纵向电流 )恰好等于物理常数ｈ ｅ2 除以一个整数ｉ(ｉ=1,2 ,3,4 ,… ) .克里青的发现后来被称为…     

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.     

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.     

量子反常霍尔效应研究进展

在没有外加磁场的作用下就能表现出量子化霍尔电导的量子反常霍尔效应已经成为霍尔家族中的重要一员,其物理起源是体能带反转结构和铁磁性相互作用.量子反常霍尔效应最重要的表现是在边缘态处具有无耗散运动的手性电流,这种性质拥有可以改变未来量子电子学的潜力,极大推动器件小型化、低损耗、高速率发展.近年来,基于理论指导,人们在实验上已多次观察到量子反常霍尔效应.在本文中,从实验层面上重点回顾了量子反常霍尔效应在铬(Cr)、钒(V)掺杂的(Bi, Sb)₂Te₃体系的研究进展,以及目前量子反常霍尔效应在其它体系中的研究现状,深入理解量子反常霍尔效应的起源和机理,最后对量子反常霍尔效应进行总结和展望.