Hopping Transport and Quantum Hall Effect

9321417 Shklovskii This theoretical project will build a qualitative theory of the quantum Hall effect including such characteristics as the widths of the diagonal conductivity peaks and the depths of the corresponding minima. The basis for this work is the generally accepted idea that the localization length diverges only at some isolated values of the filling factor. Thus, at almost all other filling factors the low temperature conductivity is determined by hopping. In the present work the steps of the Hall conductivity will be studied. The hopping corrections to the quantized values at the plateaus will be calculated. The prefactor of the hopping conductivity, which is necessary for an understanding of the universal shapes and heights of the peaks, will be investigated. This approach will be extended to the fractional quantum Hall effect including a theory of hopping transport of fractional excitations. %%% The theoretical research will study the properties of the two- dimensional electron gas in the presence of a strong magnetic field - a subject for which the Nobel prize was awarded a number of years ago. This Quantum Hall Effect has presented physicists with an exciting new state of matter which is not yet fully understood. The present research will explore a number of properties of the Quantum Hall Effect by taking a different approach (hopping conductivity) than others and for which the principal investigator is an international expert. ***