Localisation in disordered two-dimensional systems and the universal dependence on diffusion length

The authors extend the treatment by Kaveh and Mott (1981) of the effect of weak localisation on the conductivity of disordered two-dimensional systems to include the effect of magnetic and electric fields on the localisation. It is shown that the change in conductivity due to the localization depends on only one parameter, the diffusion length. This result holds irrespective of the number of independent mechanisms which individually correspond to a separate diffusion length. Their experimental values of the conductivity for different temperatures, electric fields and different magnetic fields fall on the predicted universal curve. The derived formulae for the conductivity, when few mechanisms determine the length scale, are in agreement with our experimental data, which enables us to identify the individual diffusion lengths.