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…     

Ground State for Fractional Quantum Hall Effect

We investigate the ground-state wave function for an explicit model of electronsin an external magnetic field with specific interparticle interactions. The excitationstates of this model are also given.     

Fractional Quantum Hall Effect and (2 + 1)-Dimensional Quantum Electrodynamics

By investigating the gap equation defining thefull electron propagator in the framework of (2 +1)-dimensional quantum electrodynamics, we derive thefractional quantum Hall effect at the filling factors = 1/2, 1/3, 2/5, 1/9. In particular, thevalue = 1/2 emerges as the lowest order of thedevelopment of this gap equation.     

On the Ground State Energy of the¶Fractional Quantum Hall Effect

Let I(N,R) be the ground state energy of N electrons confined to a disc of radius R with a constant magnetic field B in the perpendicular direction. We show that, in the limit and , where ν is the Landau level filling factor, we have with . The factor is obtained through the solution of an extreme-value problem in measure theory. Received: 10 November 1998 / Accepted: 27 January 1999     

Fractional Quantum Conductance Plateaus in Mosaic‐Like Conductors and Their Similarities to the Fractional Quantum Hall Effect

A simple route to generate magnetotransport data is reported that results in fractional quantum Hall plateaus in the conductance without invoking strongly correlated physics. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that the occurrence of fractional conductance values, in particular in two‐terminal measurements, does not necessarily indicate interaction‐driven physics. The importance of an independent determination of charge densities is underscored and similarities with and differences to the fractional quantum Hall effect are critically discussed.     

A new method of calculation in the Fractional Quantum Hall Effect regime

The electron-electron and electron-background interaction energies are calculated analytically for systems with up to N = 6 electrons. The method consists of describing the position vectors of electrons using complex coordinates and all the interaction energies with complex notation, whereby simplifications become possible. As is known, in this type of calculation, complicated expressions involving integrals over many variables are encountered and the trick of using complex coordinates greatly facilitates the exact calculation of various quantities. Contrary to previous analytical calculations, using complex coordinates avoids complicated trigonometric functions from appearing in the integrand, simplifying the exact evaluation of the integrals. The method we have used can be straightforwardly extended to larger systems with N > 6 electrons.     

Unconventional Fractional Quantum Hall States in a Wide Quantum Well

JETP Letters - A bilayer electron system that is formed in a 60-nm-wide GaAs quantum well and has a large difference of the electron densities in the layers has been studied. It has been found...     

Optical Conductivity of Impurity-Doped Parabolic Quantum Wells in an Applied Electric Field

The optical conductivity of impurity-doped parabolic quantum wells in an applied electric field is investigated with the memory-function approach, and the analytic expression for the optical conductivity is derived. With characteristic parameters pertaining to GaAs/Ga_1-xAl_xAs parabolic quantum wells, the numerical results are presented. It is shown that, the smaller the well width, the larger the peak intensity of the optical conductivity, and the more asymmetric the shape of the optical conductivity; the optical conductivity is more sensitive to the electric field, the electric field enhances the optical conductivity; when the dimension of the quantum well increases, the optical conductivity increases until it reaches a maximum value, and then decreases.     

Composite-Particles (Boson,Fermion) Theory of Fractional Quantum Hall Effect

A theory is developed for fractional quantum Hall effect in terms of composite (c)-bosons (fermions) without useing Laughlin’s results about the fractional charge. Here the c-particle (fermion, boson) is defined as a bound composite fermion (boson) containing a conduction electron and an even (odd) number of fluxons (elementary magnetic fluxes). The Bose-condensed c-bosons, each containing an electron and an odd number m of fluxons at the filling factor ν=1/m is shown to generate the Hall conductivity plateau value m e ²/h, where the density of c-particles, \(n_{\phi }^{(m)}\), either bosonic or fermionic, with m fluxons is given by \(n_{\phi }^{(m)}=n_{\mathrm {e}}/m\), n _e = electron density. The only assumption is that any c-fermion carries a charge magnitude equal to the electron charge e. The quantum Hall state is shown to be more stable at ν=1/3 than at ν=1.     

Quasihole Tunneling in Disordered Fractional Quantum Hall Systems

Fractional quantum Hall systems are often described by model wave functions,which are the ground states of pure systems with short-range interaction.A primary example is the Laughlin wave function,which supports Abelian quasiparticles with fractionalized charge.In the presence of disorder,the wave function of the ground state is expected to deviate from the Laughlin form.We study the disorder-driven colla.pse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state.In particular,we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.     

Effect of External Electric Field on the Proton Conductivity of Nafion Films

The current-voltage characteristics of Nafion films were studied depending on the ambient humidity, electrode voltage, and temperature. It was shown that the film can contain free (polarization current) and bound water; the latter can be completely removed under vacuum conditions. The current decreased with time at constant electrode voltage because of water removal from the film in the absence of electrochemical processes. A theoretical model in the form of the Nernst–Planck equation was considered; it describes the proton transport through the film in an electric field. The inverse problem of restoring the diffusion coefficient from the experimental proton conductivity was solved.     

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     

Fractional Quantum Hall Effect in SiGe/Si/SiGe Quantum Wells in Weak Quantizing Magnetic Fields

We have experimentally studied the fractional quantum Hall effect in SiGe/Si/SiGe quantum wells in relatively weak magnetic fields, where the Coulomb interaction between electrons exceeds the cyclotron splitting by a factor of a few XX. Minima of the longitudinal resistance have been observed corresponding to the quantum Hall effect of composite fermions with quantum numbers p = 1, 2, 3, and 4. Minima with p = 3 disappear in magnetic fields below 7 T, which may be a consequence of the intersection or even merging of the quantum levels of the composite fermions with different orientations of the pseudo-spin, i.e., those belonging to different valleys. We have also observed minima of the longitudinal resistance at filling factors ν = 4/5 and 4/11, which may be due to the formation of the second generation of the composite fermions.     

The Fractional Statistics of Generalized Haldane Wave Function in 4D Quantum Hall Effect

Recently, a generalization of Laughlin‘s wave function expressed in Haldane‘s spherical geometry is con-structed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we use non-Abelian Berry phase to anaJyze the statistics of this membrane wave function. Our results show that the membrane wave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensiona space than 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.