268 research outputs found
The Hofstadter Energy Spectrum for an Interacting 2DEG
We study the effects of the Coulomb interactions between electrons on the
Hofstadter butterfly, which characterizes the subband structure of the Landau
levels of a two-dimensional electron gas in a perpendicular homogeneous
magnetic field and a periodic lateral superlattice potential. The interactions
essentially preserve the intricate gap structure of the Hofstadter spectra, but
with a lower symmetry that depends on the filling of the Landau bands. For
short enough periods and strong enough modulation the miniband structure can be
resolved in the thermodynamic density of states.Comment: LaTeX 4 pages with 3 PostScript figures, Contribution to EP2DSXI
Nottingham August 95 to appear in Surface Scienc
The Interrelation between Incompressible Strips and Quantized Hall Plateaus
We study the current and charge distribution of a two dimensional electron
gas under strong perpendicular magnetic fields within the linear response
regime. We show within a self-consistent screening theory that incompressible
strips with integer values of local Landau-level filling factor exist for
finite intervals of the magnetic field strength . Within an essentially
local conductivity model, we find that the current density in these
intervals is confined to the incompressible strips of vanishing local
longitudinal resistivity. This leads to vanishing longitudinal and exactly
quantized Hall resistance, and to a nice agreement of the calculated Hall
potential profiles with the measured ones.Comment: 6 pages, 3 figure
Range-Dependent Disorder Effects on the Plateau-Widths Calculated within the Screening Theory of the Iqhe
We summarize the screening theory of the integer quantized Hall effect (IQHE)
and emphasize its two key mechanisms: first, the existence, in certain magnetic
field intervals, of incompressible strips, with integer values of the local
filling factor and quantized values of longitudinal and Hall resistivity, and
second, the confinement of an imposed dissipative current to these strips,
leading to the quantization of the global resistances. We demonstrate that,
without any localization assumption, this theory explains the enormous
experimental reproducibility of the quantized resistance values, as well as
experimental results on the potential distribution in narrow Hall bars. We
further demonstrate that inclusion of long-range potential fluctuations allows
to apply the theory to wider Hall bars, and can lead to a broadening of the
quantum Hall plateaus, whereas short-range disorder tends to narrow the
plateaus.Comment: 10 pages, 4 figures, paper of the invited talk at Semi-Mag 17,
Wuerzburg, German
Anisotropic scattering and quantum magnetoresistivities of a periodically modulated 2D electron gas
We calculate the longitudinal conductivities of a two-dimensional
noninteracting electron gas in a uniform magnetic field and a lateral electric
or magnetic periodic modulation in one spatial direction, in the quantum
regime. We consider the effects of the electron-impurity scattering anisotropy
through the vertex corrections on the Kubo formula, which are calculated with
the Bethe-Salpeter equation, in the self-consistent Born approximation. We find
that due to the scattering anisotropy the band conductivity increases, and the
scattering conductivities decrease and become anisotropic. Our results are in
qualitative agreement with recent experiments.Comment: 19 pages, 8 figures, Revtex, to appear in Phys. Rev.
On the Theory of Magnetotransport in a Periodically Modulated Two-Dimensional Electron Gas
A semiclassical theory based on the Boltzmann transport equation for a
two-dimensional electron gas modulated along one direction with weak
electrostatic or magnetic modulations is proposed. It is shown that
oscillations of the magnetoresistivity corresponding to the
current driven along the modulation lines observed at moderately low magnetic
fields, can be explained as classical geometric resonances reflecting the
commensurability of the period of spatial modulations and the cyclotron radius
of electrons.Comment: 5 pages, 1 figure, text and 1 figure adde
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