3 research outputs found
Hyperfine interaction induced critical exponents in the quantum Hall effect
We study localization-delocalization transition in quantum Hall systems with
a random field of nuclear spins acting on two-dimensional (2d) electron spins
via hyperfine contact (Fermi) interaction. We use Chalker-Coddington network
model, which corresponds to the projection onto the lowest Landau level. The
inhomogeneous nuclear polarization acts on the electrons as an additional
confining potential, and, therefore, introduces additional parameter (the
probability to find a polarized nucleus in the vicinity of a saddle point of
random potential) responsible for the change from quantum to classical
behavior. In this manner we obtain two critical exponents corresponding to
quantum and classical percolation. We also study how the 2d extended state
develops into the one-dimensional (1d) critical state.Comment: 9 pages, 3 figure
Landau level mixing and spin degeneracy in the quantum Hall effect
We study dynamics of electrons in a magnetic field using a network model with
two channels per link with random mixing in a random intrachannel potential;
the channels represent either two Landau levels or two spin states. We consider
channel mixing as function of the energy separation of the two extended states
and show that its effect changes from repulsion to attraction as the energy
separation increases. For two Landau levels this leads to level floating at low
magnetic fields while for Zeeman split spin states we predict level attraction
at high magnetic fields, accounting for ESR data. We also study random mixing
of two degenerate channels, while the intrachannel potential is periodic
(non-random). We find a single extended state with a localization exponent
for real scattering at nodes; the general case has also a
single extended state, though the localized nature of nearby states sets in at
unusually large scales.Comment: 18 pages, 11 tex-files and 1 ps-file of figure
Transactions
ალექსი გორგიძის დაბადებიდან 105 წლისთავისადმი მიძღვნილი შრომათა კრებული. Сборник трудов посвященный к 150 летию со дня рождения Алексея Горгидзе. The collection of works devoted to the 105th anniversary of the birth of the Alexi Gorgidz