Hall resistance of a two-dimensional electron gas in the presence of magnetic-flux tubes

Abstract

We compute the Hall and diagonal resistivities of a two-dimensional electron gas in the presence of randomly placed magnetic-flux tubes. It is found that there is a suppression of the Hall conductance below its expected value for the corresponding uniform magnetic-field case at low electron densities, in agreement with recent experiments. At densities somewhat lower than achieved thus far experimentally, we find resonances in the transport coefficients due to Landau-level structure in the flux tubes. A classical calculation of the Hall resistance reproduces the broad features of the Hall conductance for integral or half-integral numbers of flux quanta in each flux tube.