Electron-electron interactions in highly disordered two-dimensional systems

We investigate the use of three well established methods to model the electron-electron interaction correction to the conductivity in highly disordered two-dimensional systems. In order to determine the interaction correction $\delta {\sigma }_{ee}$, we use each method to fit experimental magnetoconductivity data from highly disordered Si:P $\delta$-doped two-dimensional electron systems having conductivities ranging from $k_{F}l\sim 5$ to 30. From this analysis we find that none of the three methods fits the data over the whole range of conductivities achievable. Consequently, we present a new method of extracting $\delta {\sigma }_{ee}$, based on the elimination of the interaction correction from the resistivity tensor, which is effective for extracting $\delta {\sigma }_{ee}$ over the complete range of conductivities studied. We find $\delta {\sigma }_{ee}$ between $-5.5e^2/\pi h$ and $-7.5e^2/\pi h$ at 0.5 K for our samples.