Ara Sedrakyan

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Numerical calculations of the critical exponent of the localization length
in the Chalker-Coddington (CC) model (\nu ~2.6) differ considerably from the experimental
value (\nu~ 2.38) at the integer quantum Hall transition (IQHT). We review most of models
considered recently, revile the origin of differences and the physics behind.
The difference comes from the fact, that in CC model disorder of potential is not
fully taken into account. Besides the phase factor disorder, coming from Bohm-Aharonov
phase in the magnetic field, there is a structural disorder, connected with randomness
of the position of saddle points of the random potential. At this points quantum
tunneling is happening between Fermi lakes of the electrons in the potential landscape,
which leads to change of localization length index \nu . We suggest, that interaction
between electrons and atoms at the lattice sites affect disorder character of potential
and, at the quasiclassical limit, on addition to U(1) phase disorder of CC model we
have effective one particle random network model with structural disorder .
In paper PRB.95, 125414 (2017) we propose a model for structural
disorder, where numerical simulation on the basis of transfer matrix approach give
a value \nu = 2.37 \pm 0.017, very close to the experimental value.
Currently we have developed new technique of calculations and have launched new simulations
of \nu based on S-matrix approach. Preliminary results confirm correctness of the value obtained earlier on basis of transfer matrix approach.
We discuss also the role and validity of Harris criteria in a presence of structural
disorder and argue, that the criteria should be modified.

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Alikhanyan Natonal Science Laboratory, Yerevan, Armenia
Seminar Room 0.03, ETP
Contact: Alexander Altland