Showing papers on "Landau quantization published in 1994"
TL;DR: In this article, the influence of a disclination on the spectrum of an electron or hole in a magnetic field in the framework of the theory of defects/three-dimensional gravity of Katanaev and Volovich was investigated.
222 citations
TL;DR: In this paper, the relative index of two orthogonal infinite dimensional projections is defined as the difference in their dimensions, and the relation of the charge deficiency with the notion of adiabatic charge transport is discussed.
Abstract: We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the Fredholm index of appropriate operators, discuss its basic properties, and obtain various formulas for it. We apply the relative index to counting the change in the number of electrons below the Fermi energy of certain quantum systems and interpret it as the charge deficiency. We study the relation of the charge deficiency with the notion of adiabatic charge transport that arises from the consideration of the adiabatic curvature. It is shown that, under a certain covariance, (homogeneity), condition the two are related. The relative index is related to Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the relative index is computed explicitly for all Landau levels.
198 citations
TL;DR: A Hartree-Fock approach to the CSTE's of the ferromagnetic incompressible ground state, which occurs in the quantum Hall effect at Landau-level filling factor [nu]=1, finds for Coulomb interactions that the charged spin-texture excitation energies are always smaller than theexcitation energies of localized spin 1/2 quasiparticles and quasiholes.
Abstract: We develop a Hartree-Fock approach to the charged spin-texture excitations (CSTE's) of the ferromagnetic incompressible ground state, which occurs in the quantum Hall effect at Landau-level filling factor [nu]=1. The CSTE's are the appropriate generalization of skyrmions to the situation when there is a nonzero Zeeman coupling. We find for Coulomb interactions that the charged spin-texture excitation energies are always smaller than the excitation energies of localized spin 1/2 quasiparticles and quasiholes. However, the amount by which the energy is lowered is quite small for typical experimental situations. The net spin of the CSTE's is always much larger than 1/2, suggesting that adding or removing charge from a filled Landau level rapidly degrades its spin polarization.
172 citations
TL;DR: A recent theory of a compressible Fermi-liquid-like state at Landau level filling factors nu =1/q or 1-1/ q, q even, is reviewed, with emphasis on the basic physical concepts.
Abstract: A recent theory of a compressible Fermi-liquid-like state at Landau level filling factors nu =1/q or 1-1/q, q even, is reviewed, with emphasis on the basic physical concepts.
169 citations
TL;DR: In this paper, the authors investigated Laughlin's ansatz for the ground state wave function at fractional filling of the lowest Landau level, and found the effect of an additional quadrupolar field on the free energy, and derived estimates for the thermo dynamically equivalent spherical plasma.
Abstract: In the context of the fractional quantum Hall effect, we investigate Laughlin's ansatz for the ground state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one-component plasma, we find the effect of an additional quadrupolar field on the free energy, and derive estimates for the thermo dynamically equivalent spherical plasma. In the second part of the paper, we present various methods for expanding the wave function in terms of Slater determinants, and obtain sum rules for the coefficients. We also address the apparently simpler question of counting the number of such Slater states using the theory of integral polytopes.
154 citations
TL;DR: This work uses quantum point contacts (QPCs) to locally create and probe dynamic nuclear polarization (DNP) in GaAs heterostructures in the quantum Hall regime, opening up new possibilities for mesoscopic NMR experiments.
Abstract: We have used quantum point contacts (QPCs) to locally create and probe dynamic nuclear polarization (DNP) in GaAs heterostructures in the quantum Hall regime. DNP is created via scattering between spin-polarized Landau level electrons and the Ga and As nuclear spins, and it leads to hysteresis in the dc transport characteristics. The nuclear origin of this hysteresis is demonstrated by nuclear magnetic resonance (NMR). Our results show that QPCs can be used to create and probe local nuclear spin populations, opening up new possibilities for mesoscopic NMR experiments.
130 citations
TL;DR: The statistical mechanics of an anyon gas in a magnetic field is addressed and a harmonic regulator is used to define a proper thermodynamic limit.
Abstract: The statistical mechanics of an anyon gas in a magnetic field is addressed. A harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact N-anyon ground states, where anyons occupy the lowest Landau level, contribute to the equation of state. Particular attention is paid to the interval of definition of the statistical parameter \ensuremath{\alpha}\ensuremath{\in}[-1,0] where a gap exists. Interestingly enough, one finds that at the critical filling \ensuremath{
u}=-1/\ensuremath{\alpha} where the pressure diverges, the external magnetic field is entirely screened by the flux tubes carried by the anyons.
127 citations
123 citations
TL;DR: The relation between the Laughlin state of the quantum Hall effect and the one-dimensional model with long-ranged interaction (1/ r 2 ) is discussed in this paper, by rewriting the lowest Landau level wave functions in terms of the 1D representation.
97 citations
TL;DR: In this paper, the authors compare spatial quantization by lateral potentials (quantum dots) with Landau quantisation by a magnetic field and show that the rate of electron scattering from the first excited state to the ground state of a parabolic quantum dot is one-half of the corresponding transition rate between Landau levels.
Abstract: Acoustic phonon scattering of electrons and excitons in fully quantized systems based on GaAs/${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells is studied theoretically. We compare spatial quantization by lateral potentials (quantum dots) with Landau quantization by a magnetic field. In the Born approximation, the rate of electron scattering from the first excited state to the ground state of a parabolic quantum dot is one-half of the corresponding transition rate between Landau levels. When an increasing magnetic field is applied to a dot of sizable lateral confinement, the scattering rate first increases strongly, then exhibits pronounced oscillations, and finally decreases at high fields. Exciton relaxation by phonon emission is enhanced by a magnetic field in this system. The relaxation dynamics of quantum dot excitons strongly differs from that of magnetoexcitons in quantum wells.
87 citations
TL;DR: An analytical theory for the cases of strong disorder and numerical results for the case of weak disorder are presented and the calculation of conductivity is made use of the self-consistent Born approximation generalized to the Case of two subbands.
Abstract: Magnetoconductivity of the two-dimensional electron gas occupying two size-quantization subbands is studied theoretically. When the bottoms of subbands are separated by an integer number of Landau levels, the staircases of Landau levels in both subbands are completely aligned. For such values of magnetic field the intersubband scattering is enhanced. As it was pointed out by Polyanovsky, this results in additional Shubnikov--de Haas oscillations of conductivity with magnetic field, with period depending on subband separation, and amplitude depending weakly on temperature, provided that a large number of Landau levels in each subband are occupied. In the calculation of conductivity we make use of the self-consistent Born approximation generalized to the case of two subbands. An analytical theory for the case of strong disorder and numerical results for the case of weak disorder are presented.
TL;DR: In this paper, a nonperturbative method for evaluation of the thermodynamic scaling functions in the nominal critical region of quasi-two-dimensional type-II superconductors is generalized and extended to arbitrary type- II systems.
Abstract: A recently proposed nonperturbative method for evaluation of the thermodynamic scaling functions in the nominal critical region of quasi-two-dimensional type-II superconductors is generalized and extended to arbitrary type-II systems. It is found that, in general, layered superconductors do not exhibit single-parameter scaling except in two opposite limits corresponding to two-dimensional (2D) and (an) isotropic 3D systems. Explicit, closed-form expressions for the scaling functions are constructed in these two limits. The results are found to be in good agreement with experiments and Monte Carlo simulations. The limits on the applicability of the Landau level description of fluctuations are also discussed.
TL;DR: Landau quantization of the energy bands of a carbon nanotube is calculated within the tight-binding approximation and shows oscillations with a period that is scaled by a cross section of the unit cell of the tubule, which is specified by the symmetry of the nanotubes.
Abstract: Landau quantization of the \ensuremath{\pi} energy bands of a carbon nanotube is calculated within the tight-binding approximation The energy bands do not show explicit Landau levels, but they do have energy dispersion for all values of magnetic field The energy bandwidth shows oscillations with a period that is scaled by a cross section of the unit cell of the tubule, which is specified by the symmetry of the nanotube
TL;DR: A single model is presented which represents both of the two apparently unrelated localisation problems of the title: the localisation length in a spin-degenerate Landau level and all states of a charged particle moving in two dimensions, in a random magnetic field with zero average.
Abstract: A single model is presented which represents both of the two apparently unrelated localisation problems of the title. The phase diagram of this model is examined using scaling ideas and numerical simulations. It is argued that the localisation length in a spin-degenerate Landau level diverges at two distinct energies, with the same critical behaviour as in a spin-split Landau level, and that all states of a charged particle moving in two dimensions, in a random magnetic field with zero average, are localised.
TL;DR: In this paper, energy and wavefunctions of edge states in a two-dimensional electron gas were evaluated for a finite step potential barrier model and the spectrum exhibits richer structure than observed previously for an infinite barrier model.
Abstract: Energies and wavefunctions of edge states in a two-dimensional electron gas are evaluated for a finite step potential barrier model. The spectrum exhibits richer structure than observed previously for an infinite barrier model. Surprisingly, instead of smooth Landau level bending in the vicinity of the barrier, the levels acquire a step-like form. These plateaus have a direct impact on the widths of the magnetotransport conducting channels.
TL;DR: In this paper, the quantum mechanics of a system of charged particles interacting with a magnetic field on Riemann surfaces is studied, and the degeneracy of the Landau levels of the Laughlin wave function is investigated.
TL;DR: In this paper, the magneto-resistance due to the higher-order fractional quantum Hall effect (FQHE) around v = 1 2 Landau level filling factor within the standard framework of Shubnikov-deHaas oscillations was analyzed.
TL;DR: In this article, an open semiconductor system in which electron confinement around an obstacle is obtained using a magnetic field is investigated, and the magnetic field gives rise to Landau levels, and each associated edge state circulates around the obstacle, forming a set of quantized states.
Abstract: We have investigated experimentally an open semiconductor system in which electron confinement around an obstacle is obtained using a magnetic field. The magnetic field gives rise to Landau levels, and each associated edge state circulates around the obstacle, forming a set of quantized states. Tunable constrictions are fabricated by using a technique which enables us to control transport in and out of these states, producing Aharonov-Bohm oscillations as the magnetic field is swept. Surprisingly, a strong extra oscillation with the same h/e frequency develops, phase shifted by \ensuremath{\pi} so that the frequency appears to have doubled. We explain these results in terms of charging of isolated circulating edge states.
TL;DR: The theory of phonon-assisted cyclotron resonance in quantum wells is given; cases where electrons are scattered by confined LO phonons described by the Huang and Zhu model, Fuchs-Kliewer slab modes, and Ridley's guided mode model are considered.
Abstract: The theory of phonon-assisted cyclotron resonance in quantum wells is given; we consider cases where electrons are scattered by confined LO phonons described by the Huang and Zhu model, Fuchs-Kliewer slab modes, and Ridley's guided mode model. The effect of interface phonon modes on cyclotron resonance is also studied. Extra peaks due to transitions between Landau levels accompanied by emission of confined and interface phonons in the absorption spectrum are predicted. Numerical results for frequency, field, and well-width dependence are given for parameters characteristic of GaAs/AlAs quantum wells.
TL;DR: The results suggest that the localization length exponent $
u$ is universal with respect to Landau level index and an additional periodic potential.
Abstract: Finite size corrections to scaling laws in the centers of Landau levels are studied systematically by numerical calculations. The corrections can account for the apparent non-universality of the localization length exponent $
u{}$. In the second lowest Landau level the irrelevant scaling index is $y_{\mathrm{irr}}=-0.38\pm0.04$. At the center of the lowest Landau level an additional periodic potential is found to be irrelevant with the same scaling index. These results suggest that the localization length exponent $
u$ is universal with respect to Landau level index and an additional periodic potential.
TL;DR: In this paper, the difference between the time-dependent "circular" and Landau gauges is investigated, and it is shown that only the Landau gauge generates squeezing of an initially coherent state.
TL;DR: An interpretation of recent cyclotron resonance experiments on the two-dimensional electron gas in GaAs/AlGaAs heterostructures is presented and an $f$-sum rule is derived which allows spin polarisation to be determined directly from resonance spectra.
Abstract: We present an interpretation of recent cyclotron resonance experiments on the two-dimensional electron gas in GaAs/AlGaAs heterostructures. We show that the observed dependence of the resonance spectrum on Landau level occupancy and temperature arises from the interplay of three factors: spin splitting of the cyclotron frequency, thermal population of the two spin states, and coupling of the resonances for each spin orientation by Coulomb interactions. In addition, we derive an f-sum rule which allows spin polarization to be determined directly from resonance spectra.
TL;DR: In this article, two general approaches have been used to understand Landau damping: one approach analyzes the dephasing of oscillators, and another approach explains the damping as the result of an energy drain to those oscillators that are resonant with a coherent oscillation.
Abstract: Landau damping—the damping of coherent oscillations in a system of oscillators with feedback—has been observed in many diverse systems from plasmas to quarks to the flashing of fireflies. There are two general approaches that have been used to understand Landau damping: One approach analyzes Landau damping in terms of the dephasing of oscillators. Another approach explains Landau damping as the result of an energy drain to those oscillators that are resonant with a coherent oscillation. Both approaches are studied in this paper and it is shown that while the two approaches may seem different, they are both valid descriptions of Landau damping.
TL;DR: Numerical results indicate that pure \ensuremath{\delta}-function disorder in the absence of any Landau level coupling gives rise to nonuniversal localization properties with the critical exponents in the lowest two Landau levels being substantially different.
Abstract: We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as randomly distributed scattering centers with parametrized potentials. Using a transfer matrix for a finite-width-strip geometry, we calculate the localization length as a function of system size and electron energy. The finite-size localization length is determined by calculating the Lyapunov exponents of the transfer matrix. A detailed finite-size scaling analysis is used to study the critical behavior near the center of the Landau bands. The influence of varying the impurity concentration, the scattering potential range and its nature, and the Landau level index on the scaling behavior and on the critical exponent is systematically investigated. Particular emphasis is put on studying the effects of finite range of the disorder potential and Landau level coupling on the quantum localization behavior. Our numerical results, which are carried out on systems much larger than those studied before, indicate that pure \ensuremath{\delta}-function disorder in the absence of any Landau level coupling gives rise to nonuniversal localization properties with the critical exponents in the lowest two Landau levels being substantially different. Inclusion of a finite potential range and/or Landau level mixing may be essential in producing universality in the localization.
TL;DR: In this article, the angular momenta of the quasielectrons and quasiholes are treated as distinguishable sets of Fermions, and the allowed values of the total angular momentum L can be obtained by the addition of the angular moments of the quasi-electrons and quasi-holes.
TL;DR: In this article, the existence of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field is established.
Abstract: In a high magnetic field, such that the distance between the Landau levels exceeds the exciton Rydberg, the triplet interaction term becomes the lowest state of the system. Under these circumstances, a weak pair interaction in the triplet ground state opens a new opportunity to forming the Bose-Einstein condensate and a superfluid state of excitons at a relatively high temperature. The existence of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field are established. We show that the excitation spectrum satisfies the Landau criterion for superfluidity, and discuss the observable effects of the Bose condensate of excitons.
TL;DR: It is concluded that for noninteracting electrons the universality class of the plateau transition is [ital unchanged] in the presence of a strong Landau level mixing.
Abstract: We study the effects of Landau level mixing on the critical properties of plateau transitions in the quantum Hall effect. Combining numerical results with analytical arguments, we conclude that for noninteracting electrons the universality class of the plateau transition is [ital unchanged] in the presence of a strong Landau level mixing.