Showing papers on "Landau quantization published in 1983"
TL;DR: In this paper, a simple exact solution of the Schrodinger equation for three two-dimensional electrons in a strong magnetic field, given the assumption that they lie in a single Landau level, was found, and the interelectronic spacing has characteristic values, not dependent on the form of the interaction.
Abstract: We have found a simple, exact solution of the Schr\"odinger equation for three two-dimensional electrons in a strong magnetic field, given the assumption that they lie in a single Landau level. We find that the interelectronic spacing has characteristic values, not dependent on the form of the interaction, which change discontinuously as pressure is applied, and that the system has characteristic excitation energies of approximately $0.03\frac{{e}^{2}}{{a}_{0}}$, where ${a}_{0}$ is the magnetic length.
285 citations
TL;DR: In this article, the existence of extended electronic states is demonstrated by use of the replica formalism and duality arguments, which are analogs of four-dimensional Yang-Mills theories and occur at the center of each Landau band.
Abstract: The problem of two-dimensional localization in the presence of a magnetic field is reconsidered. The existence of extended electronic states is demonstrated by use of the replica formalism and duality arguments. These states are analogs of $\ensuremath{\theta}=\ensuremath{\pi}$ vacua in four-dimensional Yang-Mills theories, and occur at the center of each Landau band. The present results complete the explanation of the integrally quantized Hall effect.
215 citations
TL;DR: Fractional quantization of the Hall effect and the two-dimensional structures in which it occurs are described in this article, where the authors show that the Hall resistance, ρ xy, approaches h/ve2 at the plateaus of the fractional occupation of the lowest Landau level.
Abstract: Fractional quantization of the Hall effect and the two-dimensional structures in which it occurs are described The fractional quantization to date has been observed in high mobility modulation-doped AlxGa1−xAs/GaAs heterostructures at high magnetic fields and low temperatures where all electrons lie in the lowest Landau level At certain fractional Landau level occupations v = p/q (q = 3, 5, 7; p = 1, 2, 3) minima and Hall resistance plateaus develop The value of the Hall resistance, ρ xy, approaches h/ve2 at the plateaus The observed phenomena and their temperature dependence suggest the occurrence of a series of correlated electron states at fractional occupation of the lowest Landau level Both two-dimensional electron and hole systems exhibit fractional quantization
202 citations
TL;DR: In this article, the Hamiltonian of a two-dimensional system of up to six interacting electrons, in the lowest Landau level, in a rectangular box with "periodic" boundary conditions, was diagonalized numerically.
Abstract: The authors have diagonalized numerically the Hamiltonian of a two-dimensional system of up to six interacting electrons, in the lowest Landau level, in a rectangular box with "periodic" boundary conditions. They find that the ground state has a pair correlation function quite different from that of a Wigner crystal, and its energy is significantly lower. They also find some indications of a downward cusp in the energy at $\frac{1}{3}$ filling.
175 citations
TL;DR: In this paper, the density of two-dimensional electrons in a strong perpendicular magnetic field and white noise potential is calculated exactly under the provision that only the states of the free electrons in the lowest Landau level are taken into account.
Abstract: The density of states of two-dimensional electrons in a strong perpendicular magnetic field and white-noise potential is calculated exactly under the provision that only the states of the free electrons in the lowest Landau level are taken into account. It is used that the integral over the coordinates in the plane perpendicular to the magnetic field in a Feynman graph yields the inverse of the number λ of Euler trails through the graph, whereas the weight by which a Feynman graph contributes in this disordered system is λ times that of the corresponding interacting system. Thus the factors λ cancel which allows the reduction of thed dimensional disordered problem to a (d-2) dimensional φ4 interaction problem. The inverse procedure and the equivalence of disordered harmonic systems with interacting systems of superfields is used to give a mapping of interacting systems withU(1) invariance ind dimensions to interacting systems with UPL(1,1) invariance in (d+2) dimensions. The partition function of the new systems is unity so that systems with quenched disorder can be treated by averaging exp(−H) without recourse to the replica trick.
128 citations
TL;DR: In this paper, a computer simulation is performed to study the localization of a two-dimensional electron system in strong magnetic fields, and the localization criterion based on the Thouless number g (L ) is employed.
Abstract: A computer simulation is performed to study localization of a two-dimensional electron system in strong magnetic fields. Scatterers with short-range δ-potentials are assumed, and the localization criterion based on the Thouless number g ( L ) is employed. It is shown that states are localized exponentially except in the vicinity of the center of each Landau level. The decay rate of the localized wave function, i.e., the inverse localization length, approaches zero smoothly at the center. This suggests that only the states just at the center of the Landau level are not localized and all the other states are exponentially localized, although the localization length is extremely large near the center. The energy range where the localization length is extremely large becomes wider with the Landau level index.
116 citations
TL;DR: In this paper, an anti-level crossing of Landau and the electric subband levels is observed in the high-mobility two-dimensional electron gas at the GaAs/(GaAl)As interface.
Abstract: Anti-level-crossing of Landau and the electric subband levels is observed in the high-mobility two-dimensional electron gas at the GaAs/(GaAl)As interface Coupling between the electron motion parallel and perpendicular to the interface is due to a small parallel component of magnetic field This novel subband spectroscopic technique determines the electric subband transition energy in this two-dimensional electron system
102 citations
TL;DR: In this article, the two-dimensional electron gas in a quantizing magnetic field for the cases of Coulomb and harmonic interactions among the electrons was studied and it was shown that the strength of the excitation gap is a strongly oscillating function of the density not unlike what is observed in the anomalous quantum Hall effect.
Abstract: We study the two-dimensional electron gas in a quantizing magnetic field for the cases of Coulomb and harmonic interactions among the electrons. Numerical solutions for the quantum states of clusters of up to five electrons show that the strength of the excitation gap is a strongly oscillating function of the density not unlike what is observed in the anomalous quantum Hall effect. We present analytic results for the case of harmonic interactions and show that the variational wave function recently proposed by Laughlin for the Coulomb problem is in fact an exact eigenstate of the harmonic problem.
89 citations
TL;DR: In this paper, the authors investigated the temperature dependence of transverse conductivity σ xx in the two-dimensional Shubnikov-de Haas oscillation minima in GaAs-Al x Ga 1-x As heterostructures at temperatures between 10mK and 1 K.
87 citations
TL;DR: In this article, a proof of the statements used by Hofstadter to characterize this recursive structure is presented, along with an interpretation for the quantum number that labels the possible gaps within the Landau level.
Abstract: For crystal electrons in two dimensions in magnetic field, each Landau level is split into subbands by a periodic potential. The dependence of the energy spectrum on magnetic field exhibits a recursive structure. For the case of a square lattice, this structure was discovered empirically by Hofstadter [Phys. Rev. B 14, 2239 (1976)]. In this paper we present a proof of the statements used by Hofstadter to characterize this recursive structure. In addition an interpretation is provided for the quantum number that, along with the Hall conductivity, labels the possible gaps within the Landau level.
TL;DR: The charge density wave state of two-dimensional electrons which occupy only the lowest Landau level is investigated in this article, where the Hartree-Fock ground-state energy is calculated by second-order perturbation theory.
Abstract: The charge-density-wave state of two-dimensional electrons which occupy only the lowest Landau level is investigated. The previous Hartree-Fock calculation by Yoshioka and Fukuyama [J. Phys. Soc. Jpn. 47, 394 (1979)] is extended to include the higher harmonics of the density wave. The correction to the Hartree-Fock ground-state energy is calculated by second-order perturbation theory. Effects of higher Landau levels are also estimated. It is found that the ground-state energy is a smooth function of $\ensuremath{
u}$, the filling factor of the lowest Landau level.
TL;DR: In this paper, the linewidth of the far infrared cyclotron resonance in the 2-D electron gas in GaAs-AlxGa1−xAs heterojunctions was shown to be correlated with the filling factor of the Landau levels.
TL;DR: In this paper, the influence of various scattering center distributions on the Landau level width and the cyclotron resonance linewidth is calculated for GaAs-AlGaAs heterostructures in high magnetic fields.
TL;DR: In this paper, the tilted field method was used to determine the electron g-factor in GaInAs-AlInAs heterojunctions using the tilted-field method and was found to be enhanced with values of |g∗| up to 15.5 compared with a bulk g ∗ = - 3.
TL;DR: In this paper, the properties of a GaAs/AlGaAs quantum well (QW) laser diode were studied under strong magnetic fields up to 30 Tesla and the spontaneous emission spectrum was found to shift toward the higher photon energy, following the shift \hbarωc/2 of the lowest Landau level.
Abstract: Characteristics of a GaAs/AlGaAs quantum well (QW) laser diode are studied for the first time under strong magnetic fields up to 30 Tesla. When field normal to QW plane is increased, the spontaneous emission spectrum is found to shift toward the higher photon energy, following the shift \hbarωc/2 of the lowest Landau level in the region of strong magnetic fields. Moreover, the emission spectrum is shown to be very little affected when magnetic fields are applied parallel to the QW plane. These results give evidence of light emission from a fully-quantized zero-dimensional carrier system in GaAs QW structures with strong magnetic fields normal to the QW plane.
TL;DR: In this article, a version of QED is developed which allows one to treat electron-photon interactions in the magnetized vacuum exactly and which allows the calculation of the responses of a relativistic quantum electron gas and include these responses in QED.
Abstract: A version of QED is developed which allows one to treat electron-photon interactions in the magnetized vacuum exactly and which allows one to calculate the responses of a relativistic quantum electron gas and include these responses in QED. Gyromagnetic emission and related crossed processes, and Compton scattering and related processes are discussed in some detail. Existing results are corrected or generalized for nonrelativistic (quantum) gyroemission, one-photon pair creation, Compton scattering by electrons in the ground state and two-photon excitation to the first Landau level from the ground state. We also comment on maser action in one-photon pair annihilation.
TL;DR: In this paper, the n = 0 → > n = 1 Landau level and 1 s −2 p + impurity transitions in GaAs were investigated up to energies above the optical phonon energy ħΩ LO and d.c.
TL;DR: In this article, the authors derived expressions describing the Hall conductivity and the thermopower of a two-dimensional system in high magnetic fields using the thermodynamic arguments, and the main attention was paid to the quantum regime, in which the Fermi energy is lying in an energy gap between two neighbouring Landau levels.
Abstract: Expressions describing the Hall conductivity and the thermopower of a two-dimensional system in high magnetic fields are derived using the thermodynamic arguments. The main attention is paid to the quantum regime, in which the Fermi energy is lying in an energy gap between two neighbouring Landau levels. It is found, in this case, that the Hall conductivity and the thermopower arise as a response of surface magnetisation currents in the sample to the applied electric field and the thermal gradient.
TL;DR: In this article, it was shown that the plateau of quantised Hall resistance in the Si inversion layer can be removed by increasing the frequency, and the Coulomb interaction between carriers can dominate as the carrier concentration is increased and background disorder becomes less important.
Abstract: The authors present results showing that the plateau of quantised Hall resistance in the Si inversion layer can be removed by increasing the frequency. Evidence is presented on hole-like behaviour at the top of a nearly full Landau level. The characteristics of the frequency dependence indicate that the Coulomb interaction between carriers is important and can dominate as the carrier concentration is increased and the background disorder becomes less important.
TL;DR: In this article, it was shown that there are no relativistic corrections to this expression, at least in the ideal case, even if the drift velocity of the electrons approaches the speed of light or the Landau level splitting approaches the electron rest-mass energy and holds despite a classical correction to the cyclotron frequency.
Abstract: The formula for the quantized Hall conductance in a two-dimensional electron gas is often derived by solving the Schr\"odinger equation for an electron in crossed electric and magnetic fields, and taking the expectation value of the current operator in its eigenstates. In this report we demonstrate explicitly, by using the Dirac equation, that there are no relativistic corrections to this expression, at least in the ideal case. This is true even if the drift velocity of the electrons approaches the speed of light or the Landau level splitting approaches the electron rest-mass energy and holds despite the appearance of a classical correction to the cyclotron frequency.
TL;DR: The resistivity, thermopower and thermal conductivity of a two-dimensional electron gas (inversion layer) in high magnetic field has been calculated using the Kubo formula.
Abstract: The resistivity, thermopower and thermal conductivity of a two-dimensional electron gas (inversion layer) in high magnetic field has been calculated using the Kubo formula. It has been found that all transport coefficients are universal functions of the reduced temperature kBT/h(cross) omega c and the reduced chemical potential mu /h(cross) omega c, provided that the thermal broadening kBT is substantially greater than the width of the Landau levels.
TL;DR: In this paper, the critical magnetic field and specific magnetisations corresponding to first order magnetisation processes are calculated in terms of the Landau free energy expansion up to sixth order in the magnetisation.
TL;DR: In this article, cyclotron resonance in n-type GaP was observed in pulsed high magnetic fields up to 140 T using far-infrared lasers as radiation sources at 119 µm and 337 µm wavelengths.
Abstract: Cyclotron resonance in n -type GaP was observed in pulsed high magnetic fields up to 140 T using far-infrared lasers as radiation sources at 119 µm and 337 µm wavelengths. When the magnetic field was applied along the axis, the second resonant peak was observed at 100 T in addition to the first peak at 23 T for a wavelength of 119 µm, the apparent anisotropy factor K * of the effective mass on the assumption of ellipsoidal band model being estimated to be 19±2. For a wavelength of 337 µm, the second peak in the absorption was observed as a broad shoulder centered at 42 T, giving a different value of K * . These observations were interpreted in terms of the camel's back structure model of the conduction band, and the band parameters were determined by a comparison of the data with calculation of the Landau levels.
TL;DR: In this article, the diamagnetic moment of the two-dimensional electron gas was calculated for finite temperature using a simple energy band model and assuming no collisional broadening of Landau levels.
TL;DR: In this article, the energy eigenvalues for electrons moving in two dimensions in the presence of a magnetic field are investigated, and it is found that quantum oscillations similar to the de Haas-van Alphen effect can occur, even with open orbits, provided the Fermi energy is not very much greater than the energy of the last closed orbit.
Abstract: The energy eigenvalues for electrons moving in two dimensions in the presence of a magnetic field are investigated. It is found that quantum oscillations similar to the de Haas-van Alphen effect can occur, even with open orbits, provided the Fermi energy is not very much greater than the energy of the last closed orbit. We also discuss the condition for effective two-dimensionality in three-dimensional systems. For closed orbits in the plane perpendicular to the field, energy gaps are found in the density of states when the Landau level spacing exceeds the bandwidth in the direction parallel to the field.
TL;DR: In this paper, the authors reported the observation of Shubnikov-de Haas oscillations in superlattices of GaInAs and InP, showing evidence of two-dimensional behavior.
Abstract: We report the observation of Shubnikov–de Haas oscillations in superlattices of GaInAs and InP, showing evidence of two‐dimensional behavior. The electron g‐factor is deduced from both the criteria for resolution of a spin splitting by comparison with the broadening parameter Γ, and from the tilted field method, and is shown to increase with increasing resolution of the Landau levels in a manner consistent with the theory of Ando and Uemura. In the ultraquantum limit, structure at ν=1/2 and ν=1/3 is observed.
TL;DR: In this paper, the conduction electron spin resonance of graphite has been investigated, using well defined near-ideal crystals and rather two-dimensional pyrolytic graphite specimens at temperatures between 100 K and 300 K. Experimental results were analyzed in accordance with the procedure developed by Feher and Kip.
Abstract: The conduction electron spin resonance of graphite has been investigated, using well defined near-ideal crystals and rather two-dimensional pyrolytic graphite specimens at temperatures between 100 K and 300 K. The effects of slight neutron irradiation on the former and of boronation on the latter were also examined. Experimental results were analyzed in accordance with the procedure developed by Feher and Kip. The g -shift data are compared with the band-theoretical calculations by McClure-Yafet and McClure; a decreasing trend with the depression of Fermi level as well as its temperature dependence is noted to be in connection with the spin-orbit splitting of the Landau level at the band degeneracy. The relaxation time is found to be a monotonously increasing function of temperature in qualitative agreement with the Elliott mechanism.
TL;DR: In this article, the ground and excited states of a simple model Hamiltonian for shallow and deep impurities are analyzed for arbitrary magnetic field strengths, and it is shown that high magnetic fields provide an efficient means to distinguish strongly localized impurity states from shallow, effective-mass-like states, irrespective of the binding energies of these states.