10 research outputs found
Hofstadter butterfly as Quantum phase diagram
The Hofstadter butterfly is viewed as a quantum phase diagram with infinitely
many phases, labelled by their (integer) Hall conductance, and a fractal
structure. We describe various properties of this phase diagram: We establish
Gibbs phase rules; count the number of components of each phase, and
characterize the set of multiple phase coexistence.Comment: 4 prl pages 1 colored figure typos corrected, reference [26] added,
"Ten Martini" assumption adde
Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?
We find that a 2D periodic potential with different modulation amplitudes in
x- and y-direction and a perpendicular magnetic field may lead to a transition
to electron transport along the direction of stronger modulation and to
localization in the direction of weaker modulation. In the experimentally
accessible regime we relate this new quantum transport phenomenon to avoided
band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea
The possibility of a metal insulator transition in antidot arrays induced by an external driving
It is shown that a family of models associated with the kicked Harper model
is relevant for cyclotron resonance experiments in an antidot array. For this
purpose a simplified model for electronic motion in a related model system in
presence of a magnetic field and an AC electric field is developed. In the
limit of strong magnetic field it reduces to a model similar to the kicked
Harper model. This model is studied numerically and is found to be extremely
sensitive to the strength of the electric field. In particular, as the strength
of the electric field is varied a metal -- insulator transition may be found.
The experimental conditions required for this transition are discussed.Comment: 6 files: kharp.tex, fig1.ps fig2.ps fi3.ps fig4.ps fig5.p
Semi-classical study of the Quantum Hall conductivity
The semi-classical study of the integer Quantum Hall conductivity is
investigated for electrons in a bi-periodic potential .
The Hall conductivity is due to the tunnelling effect and we concentrate our
study to potentials having three wells in a periodic cell. A non-zero
topological conductivity requires special conditions for the positions, and
shapes of the wells. The results are derived analytically and well confirmed by
numerical calculations.Comment: 23 pages, 13 figure
Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields
We calculate the energy band structure for electrons in an external periodic
potential combined with a perpendicular magnetic field. Electron-electron
interactions are included within a Hartree approximation. The calculated energy
spectra display a considerable degree of self-similarity, just as the
``Hofstadter butterfly.'' However, screening affects the butterfly, most
importantly the bandwidths oscillate with magnetic field in a characteristic
way. We also investigate the dynamic response of the electron system in the
far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can
be interpreted mainly in semiclassical terms, while others originate from
inter(sub)band transitions.Comment: 4 pages with 2 embeded eps figures. Uses revtex, multicol and
graphicx styles. Accepted for publication in PRB Brief Report
Quantum Hall effect in a p-type heterojunction with a lateral surface quantum dot superlattice
The quantization of Hall conductance in a p-type heterojunction with lateral
surface quantum dot superlattice is investigated. The topological properties of
the four-component hole wavefunction are studied both in r- and k-spaces. New
method of calculation of the Hall conductance in a 2D hole gas described by the
Luttinger Hamiltonian and affected by lateral periodic potential is proposed,
based on the investigation of four-component wavefunction singularities in
k-space. The deviations from the quantization rules for Hofstadter "butterfly"
for electrons are found, and the explanation of this effect is proposed. For
the case of strong periodic potential the mixing of magnetic subbands is taken
into account, and the exchange of the Chern numbers between magnetic subands is
discussed.Comment: 12 pages, 5 figures; reported at the 15th Int. Conf. on High Magnetic
Fields in Semicond. Phys. (Oxford, UK, 2002
Hall conductance of Bloch electrons in a magnetic field
We study the energy spectrum and the quantized Hall conductance of electrons
in a two-dimensional periodic potential with perpendicular magnetic field
WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak
Landau band coupling significant changes in the Hall conductance compared to
the one-band approximation of Hofstadter's butterfly are found. The principal
deviations are the rearrangement of subbands and unexpected subband
contributions to the Hall conductance.Comment: to appear in PRB; Revtex, 9 pages, 5 postscript figures; figures with
better resolution may be obtained from http://www.chaos.gwdg.d
Spektrum und Transport fuer Bloch-Elektronen im Magnetfeld
SIGLEAvailable from TIB Hannover: RA 1396(2001,3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman