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I will present a single-parameter family of models for plateau transitions in the Quantum Hall Effect, where the localization length indexes are calculated and compared against experimental data. The model is formulated as a network of scattering electrons, where the nodes are randomly distributed in real space. For the particular value of the parameter, p=1/3, the calculated value of the localization length index coincides with the experimental value on GaAs. The model can be used to describe the QHE in topological insulators, and it is argued, that the parameter p is linked to the compensation parameter K=N_A/N_D, leading to the varying value of the localization length index. Finally, we will present a Random Matrix Model, which describes the proposed model for plateau transitions.
Ph.D. in Theoretical Physics, 1978, Yerevan Physics Institute.
Doctor of Science, 1989, Yerevan Physics Institute.
Since 1989 a full Professor at the Yerevan Physics Institute.
I have held numerous visiting professorships at various top-level European and US institutions, including the Niels Bohr Institute in Copenhagen, Denmark; LAPTH in Annecy, France; Freie University in Berlin, Germany; ISSP at Tokyo University, Japan; the University of Chicago; the University of Wuppertal, University of Augsburg, Germany and Complutense University of Madrid, Spain.
Expert in non-critical string theory, in particular, string formulation of the 3D Ising model. Over the last 15 years working on the problem of Plateau transitions in QHE, Integrable models in 2D and 3D.