共查询到20条相似文献,搜索用时 15 毫秒
1.
Tohru Koma 《Journal of statistical physics》2000,99(1-2):383-459
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. 相似文献
2.
The Hall conductivity and the localization length are calculated for weakly modulated two-dimensional systems within the lowest Landau level approximation. We find that the fractal character of the Hofstadter butterfly is reflected on the coincidence in the localization and the Hall conductivity among a series of fluxes φ+2n with integers n. 相似文献
3.
The quantum Hall effect is studied numerically in modulated two-dimensional electron systems in the presence of disorder. Based on the scaling property of the Hall conductivity as well as the localization length, the critical energies where the states are extended are identified. We find that the critical energies, which are distributed to each of the subbands, combine into one when the disorder becomes strong, in the way depending on the symmetry of the disorder and/or the periodic potential. 相似文献
4.
We consider a single-band approximation to the random Schrödinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the entire spectrum of this Hamiltonian when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level in the absence of a random potential being infinitely degenerate, while the eigenfunctions corresponding to energies in the rest of the spectrum are localized. 相似文献
5.
The paper addresses details of the single-particle electron spectrum ?l(p) in narrow Coulomb channels (l is the transverse spectrum part discrete index and p is the continuous longitudinal electron momentum). The channel is said to be narrow if differences between transverse spectrum branches ?l(p) are larger than temperature. Considered are two extreme cases with respect to magnetic field. For the first case where ?F≥?ωc, the spectrum ?l(p) first calculated by Stern et al. numerically is obtained with approximate analytical analysis (here ?F is the Fermi energy of the 2D electron system ?ωc is the cyclotron frequency). In the second case the proposed formalism is extended to high magnetic fields satisfying the inequality ?F≤?ωc. Calculated results are compared with available experimental data. 相似文献
6.
M. M. Fogler A. Yu. Dobin B. I. Shklovskii 《Physica E: Low-dimensional Systems and Nanostructures》1998,1(1-4)
The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length
as a function of magnetic field
at such minima for several models of disorder (“white-noise”, short-range, and long-range random potentials). We find that
with the exponent
between one and
, depending on the model. In particular, for the “white-noise” random potential
roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data. 相似文献
7.
Tohru Koma 《Journal of statistical physics》2000,99(1-2):313-381
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. 相似文献
8.
Juan Mateos Guilarte JosMaría Muoz Porras Marina de la Torre Mayado 《Journal of Geometry and Physics》1998,27(3-4):297-332
Algebro-geometric methods are applied to the theoretical understanding of the fractionary quantum Hall effect on a periodic lattice. The fermionic Fock space of the many-electron system is precisely identified, and as a consequence, the variational Haldane-Rezayi ground state is decomposed in terms of one-particle wave functions at the first Landau level; the filling factor is thus analytically computed. Quasi-hole and quasi-particle excitations are also analyzed. The center of mass dynamics is described in terms of a section in a very subtle stable vector bundle. The Hall conductance arises as a topological invariant; namely, the slope of the vector bundle previously mentioned. 相似文献
9.
We analyze the critical behavior of the dephasing rate induced by short-range electron–electron interaction near an Anderson transition of metal–insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in 2 + ? dimensions) with numerical simulations on the Chalker–Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data. 相似文献
10.
Ferdinand Kisslinger Dennis Rienmüller Christian Ott Erik Kampert Heiko B. Weber 《Annalen der Physik》2019,531(7)
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. 相似文献
11.
We study quantum Hall interferometers in which the interference loop encircles a quantum anti-dot. We base our study on thermodynamic considerations, which we believe reflect the essential aspects of interference transport phenomena. We find that similar to the more conventional Fabry–Perot quantum Hall interferometers, in which the interference loop forms a quantum dot, the anti-dot interferometer is affected by the electro-static Coulomb interaction between the edge modes defining the loop. We show that in the Aharonov–Bohm regime, in which effects of fractional statistics should be visible, is easier to access in interferometers based on anti-dots than in those based on dots. We discuss the relevance of our results to recent measurements on anti-dots interferometers. 相似文献
12.
Magnetic field dependence of critical current for collapse of quantized Hall resistance Icr(collapse) and critical current for breakdown of dissipationless state Icr(breakdown) have been measured near the filling factor ν=4 of Landau levels in a GaAs/AlGaAs heterostructure Hall bar. The difference Icr(breakdown)−Icr(collapse) decreases against the increase and the decrease in ν from 4 and the critical behavior disappears outside of the region 3.85<ν<4.15. 相似文献
13.
The quantum dynamics of a moving particle with a magnetic quadrupole moment that interacts with electric and magnetic fields is introduced. Then, it is discussed which conditions the external fields must satisfy so that an analogue of the Landau quantization can be obtained. Finally, by dealing with the lowest Landau level associated with the magnetic quadrupole system, an analogue of the quantum Hall conductivity is obtained.
14.
Marcus Kasner 《Annalen der Physik》2002,11(3):175-252
Two‐dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many‐particle ground state and its excitations are studied in detail at fractional filling factors for spin‐polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one. 相似文献
15.
K. Takehana T. Takamasu G. Kido M. Henini L. Eaves 《Physica E: Low-dimensional Systems and Nanostructures》2006,34(1-2):148
Transport measurements in high magnetic fields have been performed on two-dimensional electron system (2DES) separated by a thin barrier layer from a layer of InAs self-assembled quantum dots (QDs). Clear feature of quantum Hall effect was observed in spite of presence of QDs nearby 2DES. However, both magnetoresistance, ρxx, and Hall resistance, ρxy, are suppressed significantly only in the magnetic field range of filling factor in 2DES ν<1 and voltage applied on a front gate . The results indicate that the electron state in QDs induces spin-flip process in 2DES. 相似文献
16.
Ady Stern 《Annals of Physics》2008,323(1):204-249
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined “anyons”, may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation. 相似文献
17.
18.
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. 相似文献
19.
Current breakdown of the integer and fractional quantum Hall effects detected by torque magnetometry
A. J. Matthews J. P. Watts M. Zhu A. Usher M. Elliott W. G. Herrenden-Harker P. R. Morris M. Y. Simmons D. A. Ritchie 《Physica E: Low-dimensional Systems and Nanostructures》2000,6(1-4)
We have developed a novel technique that enables measurements of the breakdown of both the integer and fractional quantum Hall effects in a two-dimensional electron system without the need to contact the sample. The critical Hall electric fields that we measure are significantly higher than those reported by other workers, and support the quasi-elastic inter-Landau-level tunnelling model of breakdown. Comparison of the fractional quantum Hall effect results with those obtained on the integer quantum Hall effect allows the fractional quantum Hall effect energy gap to be determined and provides a test of the composite-fermion theory. The temperature dependence of the critical current gives an insight into the mechanism by which momentum may be conserved during the breakdown process. 相似文献
20.
We fabricated a monolayer graphene transistor device in the shape of the Hall-bar structure, which produced an exactly symmetric signal following the sample geometry. During electrical characterization, the device showed the standard integer quantum Hall effect of monolayer graphene except for a broader range of several quantum Hall plateaus corresponding to small filling factors in the electron region. We investigated this anomaly on the basis of localized states owing to the presence of possible electron traps, whose energy levels were estimated to be near the Dirac point. In particular, the inequality between the filling of electrons and holes was ascribed to the requirement of excess electrons to fill the trap levels. The relations between the quantum Hall plateau, Landau level, and filling factor were carefully analyzed to reveal the details of the localized states in this graphene device. 相似文献