project title: Anderson localization and quantum Hall effect
project leader: D.E. Khmelnitskii
access given (in days): 14
access used (in days): 8
local host: Pertti Hakonen
home institution: Trinity College, Cambridge, Cavendish Laboratory, University of Cambridge
country of institution: UK
starting date (yyyy-mm-dd): 2006-06-12
The goal of the project is to study of the connection between two fundamental phenomena in quantum solid state physics: Quantum Hall Effect and Anderson localization. Professor Khmelnitskii has recently constructed the two-parameter renormalization group flow diagram to obtain the magnetic field dependence of localization length for charged particles in two-dimensional random potential at low disorder and weak magnetic fields. This approach demonstrated the periodic singularities in the localization length. The behavior of this two-dimensional system strongly resembles the dependence of the gap in the one-dimensional metal as function of the number of electrons per unit cell. This suggests that there exists the mapping of one problem to another, which can be resolved by experiments.
Possible experiments to investigate localization length and dephasing length at low temperatures were reviewed and analyzed, both from the points of views of theoretical importance as well as experimental feasibility. At present, work in graphene looks most interesting when trying to investigate the connection between Quantum Hall Effect and Anderson localization. This direction has been selected as the key direction for future research in this project.