Influence of electronic correlations on the frequency-dependent hopping transport in Si:P

At low energy scales charge transport in the insulating Si:P is dominated by activated hopping between the localized donor electron states. Thus, theoretical models for a disordered system with electron-electron interaction are appropriate to interpret the electric conductivity spectra. With a newly developed technique we have measured the complex broadband microwave conductivity of Si:P from 100 MHz to 5 GHz in a broad range of phosphorus concentration $n\mathrm{/}{n}_c$ from 0.56 to 0.95 relative to the critical value $n_c=3.5\times {10}^{18}$ cm${}^{-3}$ corresponding to the metal-insulator transition driven by doping. At our base temperature of $T=1.1$ K the samples are in the zero-phonon regime where they show a super-linear frequency dependence of the conductivity indicating the influence of the Coulomb gap in the density of the impurity states. At higher doping $n\to n_c$, an abrupt drop in the conductivity power law $\text{sig}(\omega )\sim {\omega }^{\alpha }$ is observed. The dielectric function $\text{eps}$ increases upon doping following a power law in ($1-n\mathrm{/}{n}_c$). Dynamic response at elevated temperatures has also been investigated.